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THESIS

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FEASIBILITY OF SCRAMJET TECHNOLOGY FOR AN INTERMEDIATE PROPULSIVE STAGE OF AN

EXPENDABLE LAUNCH VEHICLE

by

Michael D. Schafer

September 2002

Thesis Advisor: Stephen Whitmore Second Reader: Charles Racoosin

THIS PAGE INTENTIONALLY LEFT BLANK

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2. REPORT DATE September 2002

3. REPORT TYPE AND DATES COVERED Master’s Thesis

4. TITLE AND SUBTITLE: Feasibility of SCRAMJET Technology for an Intermediate Propulsive Stage of an Expendable Launch Vehicle 6. AUTHOR(S) Michael D. Schafer

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13. ABSTRACT (maximum 200 words)

The single largest contributor to the cost of putting objects into space is that of the launch portion. The currently available chemical rockets are only capable of specific impulse (Isp) values on the average of 300-350 seconds, with a maximum of 450 seconds. In order to improve the performance of the current families of launch vehicles, it is necessary to increase the performance of the rocket motors, and conversely the amount of propellant/oxidizer carried.

The purpose of this thesis was to determine the feasibility of employing SCRAMJET technology for an intermediate

propulsive stage of an expendable launch vehicle. This was motivated by the fact that SCRAMJETS offer a very high propulsive efficiency when compared to conventional chemical rockets. The incorporation of a SCRAMJET engine into the configuration “stack” of an expendable launch vehicle, offers the promise of increased payload mass fraction or an increase in the number of attainable orbital profiles. Analytical tools were developed using open-source software to identify launch trajectories for the SCRAMJET-enabled rocket configurations, and to determine how these would differ from conventional launch profiles. The effects of incremental increases in configuration lift and drag coefficients due to the SCRAMJET stage was analyzed. It was determined that incorporation of SCRAMJET Technology into an expendable rocket configuration offered marked improvement in performance, reduction in total launch weight, and increase operational flexibility when compared to a similarly sized conventional chemical rocket.

15. NUMBER OF PAGES 119

14. SUBJECT TERMS Launch Vehicle, SCRAMJET, pressure gradient, launch profile, launch trajectory, lift, drag, efficiency, intermediate stage propulsion

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Approved for public release; distribution is unlimited

FEASIBILITY OF SCRAMJET TECHNOLOGY FOR AN INTERMEDIATE PROPULSIVE STAGE OF AN EXPENDABLE LAUNCH VEHICLE

Michael D. Schafer

Lieutenant, United States Navy B.S., Oregon State University, 1992

Submitted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE IN SPACE SYSTEMS OPERATIONS

from the

NAVAL POSTGRADUATE SCHOOL September 2002

Author: Michael D. Schafer

Approved by: Stephen A. Whitmore Thesis Advisor

Charles M. Racoosin Second Reader

Rudolf Panholzer Chairman Space Systems Academic Group

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ABSTRACT

The single largest contributor to the cost of putting objects into space is that of the

launch portion. The currently available chemical rockets are only capable of specific

impulse ( spI ) values on the average of 300-350 seconds, with a maximum of 450

seconds. In order to improve the performance of the current families of launch vehicles,

it is necessary to increase the performance of the rocket motors, and conversely the

amount of propellant/oxidizer carried.

The purpose of this thesis was to determine the feasibility of employing

SCRAMJET technology for an intermediate propulsive stage of an expendable launch

vehicle. This was motivated by the fact that SCRAMJETS offer a very high propulsive

efficiency when compared to conventional chemical rockets. The incorporation of a

SCRAMJET engine into the configuration “stack” of an expendable launch vehicle,

offers the promise of increased payload mass fraction or an increase in the number of

attainable orbital profiles. Analytical tools were developed using open-source software to

identify launch trajectories for the SCRAMJET-enabled rocket configurations, and to

determine how these would differ from conventional launch profiles. The effects of

incremental increases in configuration lift and drag coefficients due to the SCRAMJET

stage was analyzed. It was determined that incorporation of SCRAMJET Technology

into an expendable rocket configuration offered marked improvement in performance,

reduction in total launch weight, and increase operational flexibility when compared to a

similarly sized conventional chemical rocket.

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TABLE OF CONTENTS

I. INTRODUCTION........................................................................................................1 A. PURPOSE.........................................................................................................1 B. STRUCTURE...................................................................................................1

II. CONCEPT REVIEW ..................................................................................................3 A. MOTION OF ROCKETS ...............................................................................3 B. HIGH SPEED FLIGHT ..................................................................................5 C. AIR-BREATHING ENGINES .......................................................................7

1. Advantages of Air-Breathing Designs ................................................7 2. Limitations ............................................................................................9

D. LAUNCH ECONOMICS ................................................................................9 1. Introduction..........................................................................................9 2. Microcosm Model...............................................................................10

a. Terms/Methods........................................................................10 b. Comparison of Reusable/Expendable....................................11 c. Conclusion...............................................................................14

III. CURRENT HYPERSONIC RESEARCH...............................................................15 A. MOTIVATION FOR HYPERSONIC FLIGHT.........................................15 B. UNITED STATES HYPERSONIC RESEARCH.......................................15

1. Vehicles ...............................................................................................15 2. Weapons ..............................................................................................17

a. Fast Hawk................................................................................17 b. SHMAC ...................................................................................17

C. FOREIGN HYPERSONIC RESEARCH EFFORTS.................................18 1. Australia..............................................................................................18 2. China ...................................................................................................19 3. France..................................................................................................19 4. Germany .............................................................................................19 5. Japan...................................................................................................20 6. Russia ..................................................................................................20

IV. LAUNCH SIMULATION .........................................................................................23 A. INTRODUCTION..........................................................................................23 B. EQUATIONS OF MOTION IN THE ORBITAL PLANE........................24

1. Position Vector ...................................................................................24 2. Velocity Vector ...................................................................................25

C. DYNAMIC EQUATIONS USED BY SIMULATION ...............................26 1. Orbital Energy....................................................................................26 2. Acceleration Vector............................................................................26 3. Resolution of Forces...........................................................................27

a. Gravity.....................................................................................27 b. Thrust.......................................................................................28

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c. Aerodynamic Forces ...............................................................28 d. Vehicle Mass............................................................................29

4. Generalized Equations of Motion.....................................................29 D. TRANSFORMATION FROM GAUSSIAN TO INERTIAL

COORDINATE SYSTEMS ..........................................................................30 E. ATMOSPHERIC MODEL ...........................................................................31 F. DEVELOPMENT OF AERODYNAMIC DATA .......................................31

1. Software Programs ............................................................................31 a. AeroCFD .................................................................................32 b. HyperCFD ...............................................................................33

2. Aerodynamic databases.....................................................................33 a. Subsonic Data.........................................................................34 b. Supersonic Data......................................................................36

G. LABVIEW ......................................................................................................37 1. Front Panel .........................................................................................38 2. Block Diagram....................................................................................39 3. Icon/Connector Panel ........................................................................39

H. DEVELOPMENT OF SIMULATION TOOL............................................40 1. Front Panel Clusters ..........................................................................41

a. Setup Cluster ...........................................................................41 b. Autopilot/Waypoint Cluster ....................................................41 c. Dynamic Controls/Indications Cluster...................................42

2. Order of Execution.............................................................................43 a. Sub-frame 0 .............................................................................44 b. Sub-frame 2 .............................................................................46 c. Sub-frame 5 .............................................................................47

3. Using Launch_sim_autopilot ............................................................48 a. Pegasus Launch System..........................................................48 b. Launch Trajectory...................................................................50

V. ANALYSIS CASE STUDY.......................................................................................53 A. METHODOLOGY ........................................................................................53 B. INITIAL CONDITIONS...............................................................................53 C. ATLAS III.......................................................................................................54

1. Configuration Data ............................................................................54 2. Trajectory Design...............................................................................55 3. Highlights ............................................................................................56

a. Stage 1 Burnout ......................................................................56 b. Stage 2 Burnout ......................................................................57 c. Apogee Burn............................................................................57

D. ATLAS III-SCRAM.......................................................................................60 1. Configuration Data ............................................................................60 2. Trajectory Design...............................................................................61 3. ISS Mission Highlights ......................................................................62

a. Stage 1 Burnout ......................................................................63 b. Stage 2 Burnout ......................................................................63

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c. Apogee Burn............................................................................64 4. LEO Mission Highlights ....................................................................65

a. Stage 1 Burnout ......................................................................66 b. Stage 2 Burnout ......................................................................66 c. Apogee Burn............................................................................67

E. CONCLUSIONS ............................................................................................68 1. Performance Basis..............................................................................68 2. Economic Basis...................................................................................69 3. Censere Universus ..............................................................................70

VI. FUTURE WORK.......................................................................................................71 A. INTRO.............................................................................................................71 B. SCRAMJET DEVELOPMENT PROGRAM .............................................71

VII. SUMMARY................................................................................................................73

APPENDIX A. DERIVATION OF ALGORITHMIC EQUATIONS .............................75 A. DERIVATION OF CLASSIC ORBITAL ELEMENTS ............................75

1. Semi-major Axis, a ............................................................................75 2. Eccentricity, e ....................................................................................76 3. Inclination, i ......................................................................................76 4. Right Ascension of the Ascending Node, Ω ....................................77 5. Argument of Perigee, ω ....................................................................78 6. True Anomaly, ν ...............................................................................78

B. COORDINATE SYSTEM TRANSFORMATION.....................................79 1. Position Vector (Inertial Frame) ......................................................79 2. Velocity Vector (Inertial Frame) ......................................................80

C. ESTABLISHING INITIAL CONDITIONS................................................80 1. Position Vector ...................................................................................80 2. Velocity Vector ...................................................................................81

APPENDIX B. COMPARISION OF ISS MISSION ATLAS III/ ATLAS III-SCRAM PERFORMANCE CHARACTERISTICS ..............................................83 A. ATLAS III.......................................................................................................83 B. ATLAS III-SCRAM.......................................................................................83

APPENDIX C. AERODYNAMIC DATA ..........................................................................85 A. SUBSONIC .....................................................................................................85 B. SUPERSONIC................................................................................................87

LIST OF REFERENCES ......................................................................................................89

BIBLIOGRAPHY..................................................................................................................93

INITIAL DISTRIBUTION LIST.........................................................................................95

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LIST OF FIGURES

Figure 2.1 Rocket Equation .......................................................................................................3 Figure 2.2 Specific Impulse vs. Propellant Required ................................................................5 Figure 2.3 Atmospheric Temperature Distribution....................................................................6 Figure 2.4 Subsonic Vs. Supersonic Flow .................................................................................6 Figure 2.5 Characteristic Mach Waves......................................................................................7 Figure 2.6 Propulsion Systems Comparison..............................................................................8 Figure 2.7 Velocity/Altitude Profiles of Propulsion Designs ....................................................9 Figure 2.8 Microcosm Reusable vs. Expendable Launch Vehicle Cost Model.......................11 Figure 2.9 Expendable vs. Reusable Launch Cost Over Time ................................................13 Figure 2.10 Expendable vs. Reusable Running Average Launch Cost ...................................13 Figure 2.11 Cost per Launch vs. Average Launch Rate, 2001 to 2015 ...................................14 Figure 3.1 Pegasus/X-43 Launch Configuration .....................................................................16 Figure 3.2 X-43 Mission Profile ..............................................................................................16 Figure 3.3 Fast Hawk Vehicle Design .....................................................................................17 Figure 3.4 Hyshot Shock Tunnel Test .....................................................................................18 Figure 3.6 Variable-thrust Scramjet Design ............................................................................19 Figure 3.7 Phase I/II HSFD Vehicle Deployment ...................................................................20 Figure 3.8 Hypersonic Flying Laboratory, “Kholod”..............................................................21 Figure 4.1 Gaussian Coordinate System..................................................................................23 Figure 4.2. Perifocal Coordinate System .................................................................................24 Figure 4.3 Polar/Planar Views of the Orbital Plane .................................................................25 Figure 4.4 Gravity Force Diagram...........................................................................................27 Figure 4.5 Thrust Force Diagram.............................................................................................28 Figure 4.6 Vector Force Diagram ............................................................................................28 Figure 4.7 Classic Orbital Elements ........................................................................................30 Figure 4.8 COE/Inertial Coordinate System............................................................................31 Figure 4.9 AeroCFD Front Panel Screenshot ..........................................................................32 Figure 4.10 AeroCFD Plot Examples ......................................................................................32 Figure 4.11 Hyper CFD Front Panel........................................................................................33 Figure 4.12 Hypersonic Similarity Approximations................................................................33 Figure 4.13 Notional Launch Vehicle Design .........................................................................34 Figure 4.14 Body Tube Design ................................................................................................35 Figure 4.15 Fin Design ............................................................................................................35 Figure 4.16 Launch Configuration Subsonic Data Plot ...........................................................36 Figure 4.17 Stage II Subsonic Data Plot..................................................................................36 Figure 4.18 HyperCFD Body/Fin Design ................................................................................36 Figure 4.19 Launch Configuration Supersonic Data Plot........................................................37 Figure 4.20 Stage II Supersonic Data Plot ...............................................................................37 Figure 4.21 Control Palette/Front Panel ..................................................................................38 Figure 4.22 Example Block Diagram ......................................................................................39 Figure 4.23 Example of Connector Pane Wiring.....................................................................40

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Figure 4.24 Process Flow Diagram..........................................................................................40 Figure 4.25 Setup Cluster ........................................................................................................42 Figure 4.26 Autopilot/Waypoint Control Cluster ....................................................................42 Figure 4.27 Dynamic Controls/Indications Cluster .................................................................43 Figure 4.28 Orbital Plane/Geocentric Ground Trace ...............................................................43 Figure 4.29 Initial_Conditions.vi Diagram..............................................................................44 Figure 4.30 Read_aero_data.vi................................................................................................44 Figure 4.31 Sub-frame 0 (Autopilot Calculations) ..................................................................45 Figure 4.32 Sub-frame 1 (Propagate State Vector)..................................................................46 Figure 4.33 Sub-frame 2(Launch Diagnostics)........................................................................47 Figure 4.34 Sub-frame 5(Manage S/C Mass) ..........................................................................47 Figure 4.35 User Dialog Box...................................................................................................48 Figure 4.36 X-43 Launch Configuration .................................................................................49 Figure 4.37 Propulsion Stage Data ..........................................................................................49 Figure 4.38 Reagan Test Site ...................................................................................................50 Figure 4.39 Autopilot/Waypoint Control Cluster ....................................................................50 Figure 4.40 RTS Launch Trajectory (Default Aero)................................................................51 Figure 4.41 RTS Launch Trajectory (X-43 Aero) ...................................................................51 Figure 5.1 Atlas III 1st Stage Characteristics ...........................................................................53 Figure 5.2 Atlas III...................................................................................................................54 Figure 5.3 Centaur Upper Stage ...............................................................................................55 Figure 5.4 Atlas III ISS Service Trajectory .............................................................................56 Figure 5.5 Autopilot Waypoint Values ....................................................................................56 Figure 5.6 Autopilot Weights/Initial Values............................................................................56 Figure 5.7 Atlas III Stage One Burnout ...................................................................................57 Figure 5.8 Atlas III Stage Two Burnout ..................................................................................57 Figure 5.9 Atlas III Apogee Altitude .......................................................................................58 Figure 5.10 Atlas III-SCRAM .................................................................................................60 Figure 5.11 Atlas III-SCRAM Trajectory................................................................................61 Figure 5.12 Autopilot Waypoint Values ..................................................................................62 Figure 5.13 Autopilot Weights/Initial Values..........................................................................62 Figure 5.14 Stage One Propulsion Data...................................................................................62 Figure 5.15 Stage Two Propulsion Data ..................................................................................63 Figure 5.16 ISS Mission Stage One Burnout ...........................................................................63 Figure 5.17 ISS Mission Stage Two Burnout ..........................................................................64 Figure 5.18 ISS Mission Apogee Altitude ...............................................................................64 Figure 5.19 Stage One Propulsion Data...................................................................................65 Figure 5.20 Stage Two Propulsion Data ..................................................................................66 Figure 5.21 LEO Mission Stage One Burnout .........................................................................66 Figure 5.22 LEO Mission Stage Two Burnout ........................................................................67 Figure 5.23 LEO Mission Apogee Altitude .............................................................................67 Figure A.1 Inclination..............................................................................................................76 Figure A.2 Right Ascension of the Ascending Node...............................................................77 Figure A.3 Argument of Perigee..............................................................................................78 Figure A.4 XYZ Coordinate System .......................................................................................79

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Figure A.5 Geocentric Launch Position...................................................................................80 Figure A.6 Ellipsoidal Earth Model.........................................................................................81

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LIST OF TABLES

Table 2.1 Typical spI Values ......................................................................................................4 Table 2.2 Comparison of Expendable vs. Reusable Launch Cost Factors ..............................11 Table 4.1 VI Frame Functions .................................................................................................45 Table 5.1 Final Orbit Insertion Requirements .........................................................................68 Table 5.2 Comparison of Launcher Characteristics.................................................................69 Table 6.1 AIM-54 (Phoenix) Characteristics ...........................................................................72 Table B.1 Atlas III Mass Properties.........................................................................................83 Table B.2 Atlas III Performance Characteristics .....................................................................83 Table B.3 Atlas III-SCRAM Mass Properties .........................................................................83 Table B.4 Atlas III-SCRAM Performance Characteristics ......................................................83 Table C.1 Stage I/II (No delta correction) ...............................................................................85 Table C.2 Stage II (With Fins).................................................................................................85 Table C.3 Stage II (No Fins) ....................................................................................................86 Table C.4 Delta Calculation (B.2-B.3) ....................................................................................86 Table C.5 Launch Configuration (B.1+B.4) ............................................................................86 Table C.6 Stage I/II (No Delta Correction) ..............................................................................87 Table C.7 Stage II (With Fins).................................................................................................87 Table C.8 Stage II (No Fins) ....................................................................................................87 Table C.9 Delta Calculation (B.7-B.8) ....................................................................................87 Table C.10 Launch Configuration (B.6+B.9) ..........................................................................88

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GLOSSARY OF TERMS AIAA American Institute of Aeronautics and Astronautics AKM Apogee Kick Motor AoA Angle of Attack BAMB Bending Annular Missile Body CFD Computational Fluid Dynamics CIAM Central Institute of Aviation Motors COE Classic Orbital Element DFRC Dryden Flight Research Center DOF Degrees of Freedom FAA Federal Aviation Administration FY00 Fiscal Year 2000 GRC Goddard Research Center GTO Geosynchronous Transfer Orbit HETE High Energy Transfer Experiment HFL Hypersonic Flying Laboratory ILS International Launch Services ISS International Space Station MEO Medium Earth Orbit NASA National Aeronautics and Space Administration NASDA National Space Development Agency NASP National Aerospace Plane OCA Orbital Carrier Aircraft RBCC Rocket Based Combined Cycle RTS Reagan Test Site SCRAMJET Supersonic Combustion Ramjet SHMAC Standoff Hypersonic Missile w/ Attack Capability TF3 Test-Fly-Fix-Fly TRL Technology Readiness Level US United States VI Virtual Instrument VLS Vertical Launch System WCOOA West Coast Offshore Operating Area

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LIST OF CONSTANTS, SYMBOLS, AND UNITS

pC Pressure Coefficient 2

lbft

Fv

Force 2sec

kg m⋅

0g Gravitational Acceleration at Sea Level 29.81

secm

spI Specific Impulse (sec)

M Mach # (unit-less)

drym Dry (structural) Mass (kg)

finalm Final Mass (kg)

fuelm Fuel/Oxidizer Mass (kg)

initm Initial Mass (kg)

paym Payload Mass (kg)

mfP Propellant Mass Fraction (unit-less)

barq Barometric Pressure 2

lbft

orbitR Orbital Radius (km)

exU Exhaust Velocity seckm

rV Radial Velocity seckm

Vν Tangential Velocity seckm

V∆ Velocity Change seckm

i Inclination (deg)

µ Earth Gravitational Constant 3

523.986 10

seckm

x

Ω Right Ascension of the Ascending Node (deg)

ω Argument of Perigee (deg)

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ACKNOWLEDGMENTS The author would like to acknowledge the financial support of NASA, Team

Hyper-X, for providing the funds to purchase software and hardware used during the

course of this thesis. This work was performed under Contract MIPR EO5257D.

The author would also like to thank Code RA personnel at NASA Dryden Flight

Research Center for their assistance during all research visits, Stephen Whitmore and

Charles Racoosin for their guidance, and Nancy Sharrock for her help in resolving the

numerous formatting questions that arose during the course of thesis processing.

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1

I. INTRODUCTION

A. PURPOSE

This thesis explores the feasibility of adapting supersonic combustion ramjet

(SCRAMJET) technology for the purpose of improving the performance capabilities of

future U.S. expendable launch vehicle families. This is motivated by the high propulsive

efficiency of this type of rocket compared to the more conventional chemical variants.

The objective is not to design an actual rocket system, but rather to use analysis to

identify whether the inclusion of such technology would provide a cost-justified

improvement over current design schema.

The focus here is primarily upon addressing the following questions: what is the

maximum performance of current launch vehicle configurations; what are the effects of

incremental SCRAMJET drag increases on the flight profile; how can SCRAMJET

technology be applied to improve launch vehicle performance; what is the optimal flight

profile for a launch vehicle with a SCRAMJET intermediate stage; how does this flight

profile contrast with conventional launch profiles; and what possible missions would

benefit from the use of such a launch vehicle design.

B. STRUCTURE

The thesis is split into seven sections: Concept Review, Current Hypersonic

Research, Development of Aerodynamic Data, Development of the Simulation, Analysis,

Future Work, and Summary of Results.

The Concept Review section provides a brief review of the physical principles

associated with supersonic flight, launch vehicle performance, and orbital dynamics.

This refresher is vital to the understanding of the material covered in the later sections.

Accompanying appendices provide a more rigorous mathematical-based review.

The next section gives a current snap-shot of US and international efforts in

pursuing SCRAMJET technology. Different countries are pursuing this technology not

just as a means of obtaining solutions to the problem of more efficient, lower cost space

2

transportation, but also as a means of advanced weapons design. It is significant to note

the cooperative nature of many of these efforts.

The development of the aerodynamic data necessitated the use of several software

programs, namely AeroCFD, HyperCFD and Microsoft Excel. AeroCFD and HyperCFD

from Apogee Components provided the means of creating aerodynamic rocket forms and

generating the accompanying aerodynamic data. Microsoft Excel was used to compile

the aero data into spreadsheet form, and was instrumental in the validation of the

AeroCFD/HyperCFD data.

The development of the simulation model used during the course of this thesis

also relied upon software from several vendors, and is comprised of open-source coding.

The simulation model enables the operator to dynamically alter various environmental

and launch vehicle parameters, and view these effects concurrently. Such a design

approach facilitates a greater understanding of the dynamics of launch vehicle travel

through the atmosphere.

The Analysis section contains the information obtained from the computer model

and presents the conclusions drawn from this analysis.

The Future Work section serves to identify points that were not addressed, or that

arose during the course of thesis research, as well as points needing further investigation.

Finally, the Summary briefly reviews the tools and methods used during research,

the results, and reiterates the motivation for applying SCRAMJET technology to launch

vehicles, and the approaches used toward the goal of lower-cost, higher efficiency launch

vehicle designs.

3

II. CONCEPT REVIEW

A. MOTION OF ROCKETS

When formulating his now famous equations of motion, Isaac Newton originally

considered only the case where the mass of the system was conserved. His Second Law

is also applicable where the mass of the system is not conserved, as is the case with

rocket systems. In order to develop a mathematics expression for the motion of a rocket,

one must make use of differential equations. Tsiolkovsky’s rocket equation is given in

Figure 2.1, where

V

M0

Time t

MV+∆V

mp

Time t + ∆t

pex

mdVU

dt M

=

i

0 pM M m= −p

dMm

dt≡

i

exU

00 lnsp

MV g I

M ∆ = ⋅ ⋅

⇒

V

M0

Time t

V

M0

Time t

MV+∆V

mp

Time t + ∆t

pex

mdVU

dt M

=

i

0 pM M m= −p

dMm

dt≡

i

exU

00 lnsp

MV g I

M ∆ = ⋅ ⋅

⇒

Figure 2.1 Rocket Equation

0M is the initial mass at the start of the burn, pm is the amount of propellant burned in

time dt , pmi

is the rate of change of the rocket mass, and exU is the effective exhaust

velocity of the rocket

A useful concept for evaluating the performance of any rocket design is specific

impulse ( )spI . Specific impulse is a measure of the rocket engine’s ability to deliver an

impulse ( )0

tF dt⋅∫ for a given amount of propellant, and is represented in units of

seconds. By convention, the ratio of thrust to mass-flow is divided by the earth’s

gravitational constant ( )og to give units of seconds. Instantaneously, spp

FI

m= & . spI is

indirectly related to the type of fuel/oxidizer used. Table 2.1 indicates typical spI values

for different propulsion systems.

4

Fuel Oxidizer spI (sec)

Cryogenics (LH2) Oxygen 440-460

Hypergolics (MMH) Nitrogen Tetraoxide 260-290

Solids Ammonium Perchlorate 270

Electric (Ion) -- 2,500-10k

Nuclear -- 102-103k Table 2.1 Typical spI Values

Electric propulsion systems can produce very high spI values, but do not achieve high

thrust levels. Political, environmental, and technical concerns have limited the use of

nuclear propulsion sources for all but a few deep space applications. Research into new

fuel/oxidizer mixes will not likely result in a significant increase in spI . Except for

experimental gasses, the maximum possible spI from chemical rockets has likely been

attained. What remains to be pursued is a more efficient use of existing technologies.

This is a primary motivation behind this thesis research effort.

The rocket equation can be manipulated in order to provide an expression for the

amount of fuel and oxidizer necessary to achieve a particular velocity change (delta V).

( ) 1burn

o sp

Vg I

dry payloadfuel oxidizerM M M e

∆

⋅ +

= + −

(2.1)

Important to note is the exponential relationship of the propellant load to “delta V”

( )V∆ . Also, spI has a profound effect upon launch performance. As the efficiency of

the rocket motor increases, the amount of fuel necessary to achieve the required V∆

drops significantly. Figure 2.2 provides a graphic depiction of spI versus required

propellant to place a 1000kg payload in orbit. Engine spI for several different launch

vehicles are indicated.

5

Figure 2.2 Specific Impulse vs. Propellant Required

Current engine designs have efficiencies to the left of the bend in the curve. If it is

possible to get past this “knee”, a significant reduction of propellant carried is possible.

Engines with an spI of 1000 would reduce the propellant required by the Shuttle, in order

to loft a 1000kg payload, from the current 8:1 propellant mass-fraction ( )mfP to close to

a 1:1 ratio.

B. HIGH SPEED FLIGHT

In order to have a meaningful discussion regarding the possible benefits of

operating a launch vehicle in the atmosphere at much greater than the speed of sound, a

common terminology must be agreed upon. A comparison between the characteristics of

both subsonic and supersonic flight is also needed.

The speed of sound is the speed at which molecules communicate through

pressure waves. This sound speed varies with altitude, as it is dependent upon the

composition of the atmosphere through which it travels. Mach number (M) is a unit-less

number that consists of a ratio between an object’s velocity (V) and the local sound speed

(a).

V

Ma

= (2.2)

6

The local sonic velocity is proportional to the temperature of the air. Figure 2.3 depicts

how the temperature of the atmosphere varies with altitude. Flight is defined as

supersonic for Mach numbers greater than 1.0, and hypersonic at Mach numbers greater

than 5.

Image: NASA GSFCImage: NASA GSFC

Figure 2.3 Atmospheric Temperature Distribution

An interesting aspect of supersonic flight defies common intuition. In supersonic

flow, when area is restricted, air slows down; when area expands, the air speeds up. This

is opposite from what occurs during subsonic flow. Figure 2.4 depicts the pressure

velocity relationship for each case. The reason for this derives from the fact that air is

compressible.

Figure 2.4 Subsonic Vs. Supersonic Flow

When a rocket collides with the atmosphere, the air compresses and changes in density

(think of a traffic jam, with the cars as air molecules). This leads to the formation of a

shock wave and causes a deflection in the path of the airflow. In subsonic flow the

obstacle affects the flow upstream and downstream. In supersonic flow the obstacle is a

hydrodynamic surprise and affects are only seen downstream; the upstream gas flows as

7

if the obstacle were not present. The angle these waves make with the body-plane of the

disturbing body are a function of the body’s Mach number, as depicted in Figure 2.5. A

by-product of air-flow compression is thermal build up.

Figure 2.5 Characteristic Mach Waves

C. AIR-BREATHING ENGINES

The possibility that an air-breathing engine could be used to propel a vehicle into

orbit was first envisioned almost four decades ago. It is only with recent advances in

materials technology that serious consideration has been given towards these systems to

facilitate access to space [McClinton].

1. Advantages of Air-Breathing Designs

There are several key advantages that air-breathing engines have over

conventional rockets. Air-breathers utilize atmospheric oxygen instead of an onboard

supply of oxidant, thus a smaller overall amount of fuel can be carried aboard the launch

vehicle, thereby reducing weight, size and cost.

In a conventional rocket, the mass of oxidizer carried is about six times that of the

required fuel. Rearranging the now familiar spI equation, we get an expression for spI in

terms of propellant mass:

0 0 0 06 7sp

fuel ox fuel fuel fuel

F F F FI

g m g m m g m m g m= = ≈ =

+ + & & & & & & (2.3)

By virtue of the fact that it does not need to carry an oxidizer supply, spI is increased by a

factor of 7. The exact amount of increased efficiency is dependent upon the fuel mixture

8

used. Figure 2.6 gives a visual representation of the capabilities of current propulsion

designs.

Another way of thinking about this is that an air-breathing engine, as compared to

a rocket, uses approximately one-seventh the quantity of propellant in order to produce an

equivalent amount of thrust. This allows for smaller, less costly designs, or the ability to

get greater payloads to orbit for a given total weight. Air-breathing designs also offer

increased operational flexibility compared to conventional rockets.

Image: Grif CorpeningImage: Grif Corpening Figure 2.6 Propulsion Systems Comparison

Hypersonic propulsion systems address the following NASA Aeronautics

Technology objectives [NASA GRC]:

• Objective 6: Safety - Make space travel as safe as today's air travel. Reduce the incidence of crew loss by a factor of 40 by 2010 and by a factor of 100 by 2025.

• Objective 7: Cost - Reduce the cost of taking payloads to orbit. Reduce the

cost of delivering a payload to Low Earth Orbit (LEO) by a factor of ten by 2010, and reduce the cost of inter-orbital transfer by a factor of ten by 2015. Reduce costs for both by an additional factor of ten by 2025.

• Objective 10: Technology Innovation - Develop the revolutionary

technologies and technology solutions that enable fundamentally new aerospace system capabilities or new aerospace missions

9

It remains to be realized, but hypersonic propulsion has the potential to have as great an

impact upon the way human beings live, work, and play as the advent of the airplane

nearly 100 years ago.

2. Limitations

Air-breathing engines are not a miracle cure for the difficulties of launching

objects into space. The engine inlet is designed to maintain airflow at a pre-determined

velocity/pressure profile. There are distinct regions of the flight regime where air-

breathing designs such as scramjets can operate efficiently. Supplemental propulsion

systems, such as conventional rockets, must be used in order to place the scramjet system

at the velocity/altitude profile at which the design can operate efficiently. Figure 2.7

depicts the velocity/altitude profiles where various propulsion designs could best be

utilized.

Figure 2.7 Velocity/Altitude Profiles of Propulsion Designs

Despite advances in many areas, the state of technology is still a limiting factor in

the ability to field hypersonic designs. The upper speed limit of scramjets has yet to be

determined, but it is envisioned that hypersonic designs are capable of attaining orbital

velocities. At these extreme speeds, scramjets may no longer hold an advantage over

rocket designs due to significant thermal and structural stresses.

D. LAUNCH ECONOMICS

1. Introduction

Irrespective of the performance capability of an individual class of launch

vehicles, one is able to address their various associated costs in an effort to determine

which has greater benefit than the other, and under what conditions these findings hold

Image: NASA LANGLEY

10

true. The Microcosm Reusable Vs. Expendable Launch Vehicle Cost Model [Wertz]

presented at the International Astronautics Federation Congress, in Rio de Janeiro Brazil,

in October 2000 by James Wertz serves as the basis for determining the possible

economic advantage/disadvantages of reusable/expendable launch vehicle designs. The

following paragraphs will introduce the terminology and methods used by the Microcosm

model, briefly present the model’s economic comparison of reusable and expendable

launch vehicles, and make use of these conclusions to address the feasibility of including

scramjet technology within these designs.

2. Microcosm Model

a. Terms/Methods

Wertz begins his economic comparison of reusable and expendable launch

vehicles with the following paragraph:

It is generally assumed by the community that reusable launch vehicles will dramatically reduce launch costs because you don’t “throw away the vehicle” every time it is used. However, this is usually taken as an element of faith, without any substantive analysis to support the conclusion. The example of the Space Shuttle, originally sold to Congress on the basis of dramatically cutting launch costs, suggests that this conclusion might not be accurate under realistic conditions of development and operations.

What Wertz presented was an economic model that allows the comparison between the

two different approaches. This in turn can be used to determine in what economic

environment it is feasible to pursue reusability in whole or in part of the overall launch

vehicle design.

The model developed by Wertz is presented in a purely analytic form. It

was the goal of the author (Wertz) to “clearly separate the economic model from the

conclusions based on using it.” In this manner it is possible for different users to develop

their own conclusion based upon their own experiences and assumptions. The total

launch cost model is presented in Figure 2.8. All figures which depict launch costs are

given in millions of FY00 dollars with an adjustment for inflation of 3%/yr. Complete

derivation of the Microcosm model is beyond the scope of this thesis, and readers

desiring a more thorough presentation of the economic model should refer to the source

document.

11

covlaunch development vehicle flightops re ery refurb insuranceC C C C C C C= + + + + +

Where:

launchC ≡ Total cost of launch in FY00 dollars (excludes inflation)

tdevelopmenC ≡ Amortization of nonrecurring development cost

vehicleC ≡ Reusable: Amortization of vehicle production cost Expendable: Recurring production cost (Theoretical First Unit cost reduced by learning curve)

flightopsC ≡ Total cost of flight operations per flight

eryreC cov ≡ Recurring cost of recovery (reusable only)

refurbC ≡ Refurbishment cost (reusable only)

insuranceC ≡ Cost of launch insurance

Figure 2.8 Microcosm Reusable vs. Expendable Launch Vehicle Cost Model

b. Comparison of Reusable/Expendable

Table 2.2 summarizes the differences between expendable and reusable

vehicles in the Microcosm model. Exp refers to an expendable vehicle and ReU refers to

a reusable vehicle.

Table 2.2 Comparison of Expendable vs. Reusable Launch Cost Factors

Reusable vehicles enjoy the benefit of not throwing away expensive

hardware every time the vehicle flies. At first glance, this might lead to the assumption

that reusability is always the best course of development efforts. One must be careful not

to fall into this psychological trap, as reusable vehicles tend to be more complex, robustly

12

built (possibly heavier) to withstand repeated use, and more expensive to develop.

Components that are designed for use in vehicle recovery are of little use during the

launch phase of operations. Likewise launch systems would be considered “dead weight”

during the recovery phase (that is why the Shuttle jettisons it’s external tank). By virtue

of their design philosophy, expendable vehicles enjoy a greater payload to gross lift-off

weight ratio.

In addition to lower payload capacity, reusable vehicles incur the costs of

recovery, refurbishment, and retesting/recertification. These are costs that are not borne

by expendable designs. Another item to consider is the aging of a reusable vehicle fleet.

Experience shows that as vehicles get older, more money has to be expended on

maintenance efforts, necessitating greater testing and certification efforts. The current

problems with the fuel flow liners plaguing the Shuttle fleet is a good example of what

happens when your vehicles get older [Shuttle].

Figure 2.9 shows expendable vs. reusable launch costs over time. This

most likely represents what the majority of launch vehicle manufacturers experience

during the course of a launch vehicles useful lifetime. Cost per launch drops off for both

reusable and expendable designs once the development costs are amortized. Important to

note, is that for reusable vehicles, there will come a time when it will no longer be

economically feasible to repair the vehicle, and a replacement must be sought. Currently,

the Shuttle is the only vehicle design that can be considered reusable, and the age of the

fleet is on the order of 20 years. Figure 2.10 shows expendable vs. reusable running

average launch costs.

The running average approach addresses the need to develop a

replacement vehicle around the 15-20 year point. It also prevents the steep drop in

launch cost at this point evidenced in Figure 2.9. This prevents the situation of a

customer delaying a vehicle launch until after year 15 in order to take advantage of the

“perceived” drop in launch costs, when if fact such a course of action would reduce the

launch rate and prevent amortization of the vehicles development. The fact that studies

are still being conducted in an effort to select a replacement for the Shuttle suggests that

the program managers did not budget for a Shuttle replacement during its development.

13

Figure 2.9 Expendable vs. Reusable Launch Cost Over Time

Figure 2.10 Expendable vs. Reusable Running Average Launch Cost

The biggest influence upon the cost of a launch vehicle is the number of

launches that occur per year. Figure 2.11 gives the cost per launch vs. the average launch

rate over a fifteen-year period from 2001-2015. The point to take away from the figure is

that as the number of launches per year increases, the associated cost for each launch will

decrease. This reduction in launch cost is enjoyed for both reusable and expendable

vehicle designs.

14

Figure 2.11 Cost per Launch vs. Average Launch Rate, 2001 to 2015

c. Conclusion

Wertz concludes that unless the launch rate is significantly greater than

100 vehicles per year, expendable vehicles will continue to enjoy a “significant economic

advantage” over reusable vehicles. Assuming that the model costs are realized, a drop in

expendable vehicle launch costs by a factor of 5-10 should be possible. This advantage is

due in part to the fact that expendable vehicles do not have to account for

recovery/refurbishment costs, are able to incorporate new technology and upgrades more

easily than reusable designs, and that flight operations for expendable vehicles are in

general less complex than for reusable vehicles.

Once it is accepted that expendable vehicles provide an economically

viable means of delivering payloads to orbit, the question must be asked is it possible to

improve further. Scramjet engines have potential spI values well to the right of the curve

in Figure 2.2. If a scramjet is incorporated into the launch stack of an expendable design,

there is the potential of reducing the total launch-mass of the vehicle by approximately

half.

15

III. CURRENT HYPERSONIC RESEARCH

A. MOTIVATION FOR HYPERSONIC FLIGHT

The possibility that an air-breathing engine could be used to propel a vehicle into

orbit was first envisioned almost four decades ago. As early as 1948, engineers at

Dryden Flight Research Center were conducting flight tests with vehicles such as the Bell

XS-1 at speeds greater than Mach 1. In 1952, preliminary studies were begun that

attempted to address problems associated with spaceflight. The X-15, which holds the

current world records for altitude and speed for winged aircraft, last flew in 1968.

Despite several efforts, no usable hypersonic vehicle was developed for the next four

decades. Dr. Richard P. Hallion, chief historian for the U.S. Air Force, observed that

early hypersonic technology was in effect ahead of its time. Quoted in a 19 August 1997

New York Times article, Dr. Hallion commented [CDISS]:

When you look at the hypersonic work of the 50's and 60's, a lot of it was really very good, far in advance of its time. What was not advanced was the ability to develop the structures, materials, propulsion, guidance and controls to make operational vehicles based upon the research. We can contemplate vehicles today that are far more practical to develop than in the 1960's, when much of the pioneering work was done.

With recent advances in material science, designs that were once considered impractical

may hold the key to providing cheaper access to space.

B. UNITED STATES HYPERSONIC RESEARCH

1. Vehicles

The United States current research efforts into hypersonic vehicles focus upon the

X-43 series of vehicles, collectively dubbed “Hyper-X.” This program owes much of its

legacy to the National Aerospace Plane (NASP). The NASP was supposed to

demonstrate hypersonic-to-orbit flight, but was cancelled in 1993 [Aerospaceguide]. The

Hyper-X test vehicles will be 12 ft (3.6 m) in length and have a wingspan of 5 ft (1.5 m).

They will employ a hydrogen-fueled ramjet/scramjet. The Pegasus booster built by

Orbital Sciences Corporation of Chandler, Arizona accelerates the X-43 to launch

16

velocity (Mach 7). The Pegasus and attached X-43 are carried aloft by NASA Dryden’s

B-52 “Mothership”, depicted in Figure 3.1.

Figure 3.1 Pegasus/X-43 Launch Configuration

Figure 3.2 depicts the planned X-43 mission profile. Following release from the

B-52 “Mothership,” the Pegasus booster delivers the X-43 to test altitude and airspeed.

Upon booster burnout, the X-43 enters free flight and the Scramjet engine ignites.

Following the powered-flight portion of the test, the X-43 is maneuvered to dissipate

speed/energy and arrive at the desired impact area.

Figure 3.2 X-43 Mission Profile

The first flight of the X-43A occurred on June 2nd, 2001. Five seconds into flight,

the Pegasus booster went out of control. Subsequently, Flight Controllers destroyed both

vehicles [Edwards AFB]. NASA engineers are currently working with industry to refine

the X-43 design. Two other variants of the X-43 are planned. The X-43C will be

increased in length by four feet in order to accommodate its hydrocarbon fuel source.

The X-43B will be a propulsion demonstrator for a rocket-based combined cycle (RBCC)

17

engine design. Unlike the X-43A/C variants, the X-43B will not need the Pegasus

booster [Soppet]. It will be able to switch between rocket mode and scramjet modes of

operation.

2. Weapons

a. Fast Hawk

In support of the Department of Defense’s (DoD) Joint Warfighter

Precision Force vision, the Office of Naval Research is sponsoring research into a

hypersonic follow-on design to the Tomahawk cruise missile. The Low-Cost Missile

ATD, commonly known as Fast Hawk, seeks to demonstrate a unique, finless, low-drag

bending annular missile body (BAMB) airframe and ramjet propulsion concept to give

the Navy the capability to attack time-critical and hardened targets [MILNET]. In this

concept, depicted in Figure 3.3, the ramjet combustor and tandem booster are connected

to the frontal missile airframe by an articulating thrust vector control joint.

Figure 3.3 Fast Hawk Vehicle Design

b. SHMAC

The Air Force’s AF2025 study envisions a hypersonic attack missile as a

critical component in ensuring the Air Force’s ability to achieve Global Reach/Global

Power [USAF]. The Standoff Hypersonic Missile with Attack Capability (SHMAC), is

envisioned as a Mach 8 weapon driven by a combined rocket/scramjet (RBCC)

propulsion system, capable of being launch from either aircraft, ship-based vertical

launch system (VLS) tubes, or mobile or fixed ground sites. A modular payload design

will allow for a maximum of flexibility in highly fluid future combat situations.

18

C. FOREIGN HYPERSONIC RESEARCH EFFORTS

Foreign efforts into hypersonic research can best be characterized as a

multinational effort. No individual country has the economic might to individually

challenge the United States. In view of the current austere budgetary environment, even

the US is beginning to adopt such a cooperative development arrangement.

1. Australia

Australia leads a multinational hypersonic flight project involving personnel from

Great Britain, Germany, South Korea, Japan, and the United States. HyShot is the

University of Queensland initiative that seeks to establish a correlation between pressure

measurements of an axis-symmetric scramjet design made in the University of

Queensland T4 shock tunnel (Figure 3.4) and those actually experienced in flight. The

Figure 3.4 Hyshot Shock Tunnel Test

HyShot Program uses a two-stage Terrier-Orion Mk70 rocket to boost the payload and

the empty Orion motor (the Orion motor remains attached to the payload) to an apogee of

approximately 330km. As the spent motor and its attached payload fall back to Earth,

they gather speed, and the trajectory is designed so that between 35km and 23km, they

are traveling at Mach 7.6 [HYSHOT].

The HyShot Program secured its place in history with the first successful flight

test of supersonic combustion [History]. Future flight trials will seeks to develop an

engine design with a net positive thrust.

19

2. China

Information regarding China’s hypersonic program is extremely sparse A September 17,

2001 news article stated that Chinese researchers were currently working on an aircraft

capable of flying at five times the speed of sound. The Xinhua news agency quotes the

Chinese Academy of Science as saying, “A Chinese 'hypersonic' aircraft, able to cover

6,105 kilometers an hour, could be developed in 10 to 15 years [Airwise].

3. France

France is a recognized leader in high-speed engine design. They currently field a

ramjet-propelled cruise missile (ASMP) capable of Mach 3.5, with plans for a follow-on

version capable of Mach 5+ [CDISS]. France entered into a partnership with the

Moscow Aviation Institute in 1995. The goal of the partnership is to produce a variable-

thrust scramjet engine, depicted in Figure 3.6, with performance in the Mach 2-12 range.

The tests are similar to those being performed by NASA’s Hyper-X program.

Figure 3.6 Variable-thrust Scramjet Design

France has also engaged in joint research with Germany to develop a hypersonic

surface to air missile for air defense purposes, and will cooperate with Japan’s National

Space Development Agency (NASDA) to conduct the flight-testing of the Japanese

unmanned shuttle design, dubbed HOPE-X.

4. Germany

Germany has recently tested flown a hypersonic experimental missile (HFK),

reaching speeds of greater than Mach 6 [Jane's Missiles and Rockets]. The test

established the performance of a conical-shaped engine designed by the French

Corporation EADS. EADS/LFK chief executive officer Werner Kaltenegger said,

“Using the hypersonic test bed, we are able to investigate a broad variety of technical and

physical phenomena in the high-speed range which will be of advantage to future

applications.” Further flight-testing of the HFK is expected to occur in 2003.

20

5. Japan

Japan has entered into an agreement with the French Space Agency (CNES) to

conduct high-speed flight tests, as a part of Japan’s H-II Orbiting Plane Experiment

(HOPE-X) program, to develop a reusable space transportation system [CNES-NASDA].

The two-phase High-Speed Flight Demonstration (HSFD) program is scheduled to begin

in 2002. The first phase of the program will use a jet engine powered flight vehicle to

verify the autonomous landing system design. Phase II will validate the aerodynamic

tools used to predict vehicle-handling characteristics during transonic flight, using a 25%

scale model (Figure 3.7) of the HOPE-X vehicle dropped from a stratospheric balloon.

Both experiments will be performed at the Esrange test site in Sweden.

Figure 3.7 Phase I/II HSFD Vehicle Deployment

6. Russia

In the 1990s, the Russians began conducting tests of hydrogen-fueled

ramjet/scramjet engines as part of a high-speed flight program. In November 1994,

Russia’s Central Institute of Aviation Motors (CIAM) entered into a partnership with

NASA in an effort to determine the maximum Mach number at which a scramjet can be

expected to operate [AIAA-96-4572]. The Hypersonic Flying Laboratory (HFL),

“Kholod,” shown in Figure 3.8 below, carries aloft this axisymmetric scramjet design.

On February 12, 1998, a launch was conducted at the Sary Shagan test range in central

Kazakhstan. During the test, the HFL achieve a maximum velocity greater than Mach

6.4 [NASA/TP-1998-206548].

21

Figure 3.8 Hypersonic Flying Laboratory, “Kholod”

22


23

IV. LAUNCH SIMULATION

A. INTRODUCTION

As part of this thesis, it was necessary to develop a method of simulating a rocket

launch. The goal was to be able to take a snapshot of the dynamic conditions

experienced by the launch vehicle at any point in time. The end product is 3 degree of

freedom (DOF) simulation, which models radial velocity ( )rV , tangential velocity ( )Vν ,

radius ( )r , true anomaly ( )ν , and mass ( )m . The differential equations used to describe

the orbital motion of the spacecraft are derived using the satellite or Gaussian coordinate

system [Vallado]. In this coordinate system, the r-component points away fro mthe

center of the Earth in a radial direction, the -componentν is perpendicular to the radial

direction and points in the direction of travel of the spacecraft, and the -l component

completes the right-handed orthogonal coordinate system. This coordinate system stays

fixed to the spacecraft at all times, and the -l component is always perpendicular to the

instantaneous orbit. The Gaussian coordinate system is depicted in Figure 4.1.

Figure 4.1 Gaussian Coordinate System

The National Instruments software program LabVIEW was used to code the

launch simulator. LabVIEW operates on the principle of data flow, vice traditional top-

down software design methodologies. This approach enables the user to create virtual

instruments with little or no programming language experience.

24

B. EQUATIONS OF MOTION IN THE ORBITAL PLANE

Figure 4.2 depicts the Perifocal Coordinate System used in establishing the

equations of motion. True anomaly, ν , describes the orbital position of the vehicle with

respect to perigee (covered further in section B).

Figure 4.2. Perifocal Coordinate System

1. Position Vector

The polar form of the position vector, Rv

, is represented by

00

R

R =

v (4.1)

The Cartesian form of the position vector is

( )( )

cossin

0

x

y

z

R rR rR

νν

=

(4.2)

The orbital radius can also be described in terms of the equation of an ellipse

( )

21

1 cos

a eR

e ν

− =+

(4.3)

25

2. Velocity Vector

The velocity vector, Vv

, has both radial an tangential components represented as

0

rV

V Vν

=

v (4.4)

where: vehicle flight path angle (deg)γ =

( )sinrV V γ=v

(4.5)

( )cosV Vν γ=v

(4.6)

The Cartesian form of the velocity vector is

( ) ( )( ) ( ) ( ) ( )

( ) ( )

cos sin 0cos sin

sin cos 0sin cos

0 0 1 0

x rr

yr

z

V VV V

V v VV V

V

νν

ν

ν νν ν

νν ν

− − = = +

(4.7)

Although the above equations allow for a component of velocity in the z-direction, only

in-plane motion is utilized in the simulation. Figure 4.3 provides overhead and side

views of the orbital plane.

Figure 4.3 Polar/Planar Views of the Orbital Plane

26

C. DYNAMIC EQUATIONS USED BY SIMULATION

1. Orbital Energy

In an ideal Keplerian world, the specific orbital energy, ε , is constant.

2orbit

orbitaµ

ε = − (4.8)

If a non-conservative force is performing work on the vehicle operating in the

orbit “a”, after a period of time t, the new orbital energy level is

[ ] ( ) ( )0

2 2orbit t

orbit orbit vehiclet

Energy changea a mµ µ

ε = − = − + (4.9)

With this in mind, Kepler’s Laws no longer apply, and Newton’s Laws must be used to

describe these orbits:

Velocity R

V Rt

ω∂

= + ×∂

vv vv (4.10)

Acceleration externalF VV

M tω

∂= + ×

∂∑

v v vv (4.11)

Mass-change thrustvehicle

o sp

FM

g I= −

⋅& (4.12)

2. Acceleration Vector

Since the coordinate system is moving with the orbiting spacecraft, the effects of

the angular motion of the spacecraft must be accounted for. Therefore, the inertial rate of

change of the vehicle’s velocity vector is given by the vector Av

, where

2

0 0

rr

VrV

V VA V

r

ν

νν

−

= +

&v & (4.13)

27

[Friedberger]. Newton’s Second Law gives an expression for the force acting upon an

object as the object’s mass multiplied by the objects acceleration, or

F m A= ⋅vv

(4.14)

After some rearrangement of terms, it can be seen that the change in the vehicle’s

velocity is given by the expression

2

r

r

VV F r

mV V Vr

ν

ν ν

−

= −

v&& (4.15)

3. Resolution of Forces

The force acting upon the launch vehicle can be broken down into four broad

categories: gravity, thrust, and aerodynamic forces. As with the acceleration vector, each

of these forces has a component in the radial ( )r direction, and the tangential

( )ν direction.

a. Gravity

gravFv

rv

m

M

y

x

gravFv

rv

mm

M

y

x

Figure 4.4 Gravity Force Diagram

The force of gravity is a conservative force. That is to say that it neither

removes, nor adds energy to the orbit. Gravity is subject by the “inverse-square” law,

which states that the force varies as a function of 2

1

r, and is represented by

28

2

0

gravFr

m

µ − =

v (4.16)

b. Thrust

v

thrustF Figure 4.5 Thrust Force Diagram

Thrust is a non-conservative force that adds or removes energy from an

orbit. A simplifying assumption is that thrust always acts along the direction of the

longitudinal axis of the vehicle. The force due to vehicle thrust is given by the equation

4.17.

( )

( )

sin

cos

thrust thrust

rthrust

thrustthrust

F FmF m

Fm Fmm ν

θ

θ

= =

v (4.17)

c. Aerodynamic Forces

Figure 4.6 Vector Force Diagram

29

The aerodynamic forces, lift and drag, are non-conservative forces that

remove or add energy to the vehicle’s orbit. The lift force acts perpendicular to the total

velocity vector, and the drag force opposes the total velocity vector. The aerodynamic

forces are

( ) ( )

( ) ( )cos sin

cos sinr

aero

F Lift DragF Drag Liftν

γ γγ γ

⋅ − ⋅ = − ⋅ − ⋅

(4.18)

where flight path angleγ =

This expression can in turn be rewritten in terms of the total velocity vector

[ ]

2 2

2 2

r

r r

aero r

r

V Lift VDrag

F V VF V Drag V Lift

V V

ν

ν

ν ν

ν

− + =

− +

+

(4.19)

d. Vehicle Mass

The rate of change in the vehicle’s mass over time is given as

thrustvehicle

o sp

Fm

g I= −

⋅& (4.20)

The total mass of the vehicle at any point in time can be found by integrating the rate

change over the interval of time and deducting this from the vehicle’s initial mass

00

tthrust

to sp

FM M

g I= −

⋅∫ (4.21)

4. Generalized Equations of Motion

It is now possible to describe the generalized equations of motion as a collection

of the individual calculations previously performed

30

( )

( ) ( ) ( ) ( )

( )( ) ( ) ( )

( )

2

2

0

cos cos sinsin

cos sin coscos

sin

thrust

r r thrust

r

thrust

sp

Lift DragV Fr m mr

V Drag LiftV V FV r m m

Liftht m Vr V

Vm r

Fg I

ν

ν

ν

ν

ν

γ φ γµθ

γ γ φθ

φ

ν

⋅ ⋅ − ⋅ − + ⋅ +

⋅ + ⋅ ⋅ ⋅ − + ⋅ − ∂ ⋅ −=∂ ⋅

− ⋅

&&

&&&

(4.22)

D. TRANSFORMATION FROM GAUSSIAN TO INERTIAL COORDINATE

SYSTEMS

Because of significant non-conservative external forces (i.e. lift, drag, thrust) will

be acting on the spacecraft, the instantaneous orbit will no longer remain constant. Thus

the instantaneous orbit must be computed from the Gaussian on in-plane velocity and

position vectors. The set of six classic orbital elements (COE) used to describe the

instantaneous orbit with respect to the inertial coordinate system are

Semi-major Axis Eccentricity Inclination

Right Ascension of the Ascending Node Argument of Perigee True Anomaly

aei

ων

−−−

Ω −−−

Figure 4.7 Classic Orbital Elements

These orbital parameters, and the inertial coordinate system, are depicted in Figure 4.8.

Appendix C presents the transformations that allow the reader to compute the orbital

parameters from the inertial velocity and position vectors.

31

Figure 4.8 COE/Inertial Coordinate System

E. ATMOSPHERIC MODEL

The effects of lift and drag on the vehicle will be greatly dependent upon the

vehicle’s position within the Earth’s atmosphere. For this analysis the 1976 standard

atmosphere was used [NOAA].

Because the Earth’s atmosphere is rotating with respect to the inertial coordinate

frame, the rotation must be accounted for in order to obtain high accuracy in the lift and

drag calculations. With respect to the inertial coordinate system, the rotational velocity

of the atmosphere is expressed as the inner product of the inertial position vector, and the

angular velocity of the Earth. This computed velocity vector due to Earth-rotation was

then subtracted from the inertial velocity vector to give an estimate of the “wind-relative”

velocity vector of the vehicle.

F. DEVELOPMENT OF AERODYNAMIC DATA

1. Software Programs

Several software programs were utilized in the development of the tools required

during the course of this thesis research. AeroCFD and HyperCFD from Apogee

Components provided the means of creating aerodynamic rocket forms and generating

the accompanying aerodynamic data. Microsoft Excel was used to compile the aero data

into spreadsheet form, and was instrumental in the validation of the AeroCFD/HyperCFD

data.

32

a. AeroCFD

AeroCFD is a program that evaluates the aerodynamic qualities of a rocket

design. The user is able to create original vehicle designs, or select from several stock

rocket designs. From these designs, aero data can be generated for varying subsonic

airspeeds and angles of attack (AOA). The AeroCFD user interface is depicted in Figure

4.9 below. The user is also able to select between compressible and non-compressible

Figure 4.9 AeroCFD Front Panel Screenshot

fluid flow cases. AeroCFD uses the Prandtl-Glauret rule to estimate the effects of

compressibility on air pressure and air velocity.

Once the aerodynamic data are generated for the rocket design, flow

visualization can be accomplished. The user is provided with options for displaying

velocity vector/contour plots, and static/dynamic pressure contour plots. Examples of the

plots options are depicted in Figure 4.10.

Figure 4.10 AeroCFD Plot Examples

33

b. HyperCFD

HyperCFD performs similar functions for flight regimes in the transonic

region above Mach one. Once the vehicle design is finalized, aerodynamic data can be

obtained for speeds greater than Mach 1.05. The US Standard Atmospheric Data (1962)

is used for variation of pressure/density with changing altitude. Figure 4.11 depicts the

HyperCFD front panel. HyperCFD makes use of the hypersonic similarity law to

approximate the pressure coefficient (Cp) slightly above the transonic region (M > 1.05)

[Hamaker]. Experimental pressure distribution results support this modification over a

wide range of Mach numbers. A visual depiction of these results is given in Figure 4.12.

Figure 4.11 Hyper CFD Front Panel

Figure 4.12 Hypersonic Similarity Approximations 2. Aerodynamic databases

Figure 4.13 depicts the individual stages and combined configuration for the

notional launch vehicle. An axis-symmetric scramjet design was incorporated into the

34

second stage of the vehicle. This choice was made in an effort to avoid some of the

problems associated with an asymmetric body-integrated design. The axis-symmetric

design is easier to integrate into the launch stack, provides better heat dissipation (more

uniform surface) than the body-integrated design, and most importantly is far more

aerodynamically stable than an asymmetric design.

Total Configuration

Total Configuration(without fins)

Stage 2 (with Fins) Stage 2 (without Fins)-

=+

Total Configuration

Total Configuration(without fins)

Stage 2 (with Fins) Stage 2 (without Fins)-

=+

Figure 4.13 Notional Launch Vehicle Design

In order to determine the feasibility of SCRAMJET technology for an

intermediate propulsive stage of an expendable launch vehicle, it was necessary to

generate subsonic (M<1) and supersonic (M>1) aerodynamic data. These data were

developed using AeroCFD for the subsonic case, and HyperCFD for the supersonic case.

CN and CD are based upon the nose area of the vehicle. The calculations were repeated

for each Mach and alpha. Units of meters, Newtons, and seconds (m-nt-sec) were carried

throughout both programs.

a. Subsonic Data

The first step in obtaining the subsonic data was to define the body tube

geometry of the notional launch vehicle. The program allows the user to select standard

tube geometry or a free-form option. Figure 4.14 depicts the user interface. The user

selects the basic nose cone shape from a pull-down menu and inputs dimension of the

nose cone length, diameter and body tube length. The next step is to establish the number

and configuration of fins (Figure 4.15) on the vehicle. Once the design of the vehicle is

35

completed, a solution for the complex fluid-flow is determined. The user then has the

option of plotting these results, or modifying the vehicle geometry prior to resolving.

Figure 4.14 Body Tube Design

Figure 4.15 Fin Design

For designing the notional SCRAMJET launch vehicle, the free-form option was chosen.

A conical nose cone shape was selected to approximate the inlet design of the

SCRAMJET engine.

Flow solutions were computed for three components of the launch vehicle:

launch configuration, stage II (with fins), and stage II (w/o fins). The later two designs

were necessary to overcome the limitation of AeroCFD not allowing for multiple stage

designs. The fins/sans fins designs were used to determine the “delta” correction that had

to be added to the launch configuration CFD results. Data were obtained for angles of

attack (AoA) of 0, 1, 2, 3, 5, 8, 10, and 15 degrees and velocities of 0, .2, .5, .7, and .8

36

Mach. Figure 4.16 depicts the launch configuration Cn/Cd subsonic data. Figure 4.17

depicts the Stage II (scramjet) Cn/Cd subsonic data. The tabular data are contained in

Appendix B (Aerodynamic Databases).

Cn/Cd vs. Alpha

0

2

4

68

10

0 1 2 3 5 8 10 15

Alpha (deg)

Cn/

Cd

Cn/Cd(0)Cn/Cd(.2)Cn/Cd(.5)Cn/Cd(.7)Cn/Cd(.8)

Figure 4.16 Launch Configuration Subsonic Data Plot

Cn/Cd vs. Alpha (Stage II)

0

2

4

6

8

0 1 2 3 5 8 10 15

Alpha (deg)

Cn/

Cd Cn/Cd(0)

Cn/Cd(.2)Cn/Cd(.5)Cn/Cd(.7)

Cn/Cd(.8)

Figure 4.17 Stage II Subsonic Data Plot

b. Supersonic Data

HyperCFD was used to develop the supersonic aerodynamic data for the

design. It was necessary to first establish the body geometry, then fin layout in a process

similar to that used with AeroCFD. The interface is depicted in Figure 4.18.

Figure 4.18 HyperCFD Body/Fin Design

37

Although both programs are developed by Apogee Components, the model developed for

one was not transferable to the other. The same overall dimensions were used for the

supersonic model as for the subsonic case. Minor differences in the body shape between

the two designs were assumed to be negligible. Data were obtained for angles of attack

(AoA) of 0, 1, 2, 5, and 8 degrees and velocities of 1.2, 1.5, 2, 5, 8, and 10 Mach. Figure

4.19 depicts the launch configuration Cn/Cd supersonic data. Figure 4.20 depicts the

Stage II (scramjet) Cn/Cd supersonic data. The tabular data can be found in Appendix B

(Aerodynamic Databases).

Cn/Cd vs. Alpha (Launch Config.)

0

1

2

3

4

0 1 2 5 8

Alpha (deg)

Cn/

Cd

Cn/Cd(.12)Cn/Cd(1.5)Cn/Cd(5)Cn/Cd(8)Cn/Cd(10)

Figure 4.19 Launch Configuration Supersonic Data Plot

Cn/Cd vs. Alpha (Stage II)

0

0.5

1

1.52

2.5

0 1 2 5 8

Alpha (deg)

Cn/

Cd

Cn/Cd(1.2)Cn/Cd(1.5)Cn/Cd(2)

Cn/Cd(5)Cn/Cd(8)Cn/Cd(10)

Figure 4.20 Stage II Supersonic Data Plot

G. LABVIEW

The simulation serves to provide insight as to which parameters are important to

the problem. Batch simulations programmed using LabVIEW are capable of performing

extended Monte-Carlo analyses. The ”piloted” simulation tool can be used for generating

feasible starting trajectories for subsequent optimization codes, such as POST and DIDO

[Fahroo].

38

National Instruments LabVIEW (Laboratory Virtual Instrument Engineering

Workbench) is a computer-based development environment leveraged upon graphical

programming. LabVIEW makes use of graphical symbology to describe individual

programming steps. The program’s ease of use is largely due to its use of familiar

scientific terminology, symbols, and ideas. LabVIEW supports communication with

typical laboratory hardware, and plug-in data acquisition boards. The software comes

with a tutorial complete with a glossary of terms, learning activities, and support

resources.

Programs created in LabVIEW are referred to as Virtual Instruments (VIs). A VI

makes use of functions to manipulate data from a variety of sources and display the

results for the user. Each VI consists of three basic components: the Front Panel, the

Block Diagram, and the Icon/Connector Pane.

1. Front Panel

The front panel is the user interface to the virtual instrument (VI). The panel is

built using controls and indicators the user selects from the Control Palette. Controls

serve as inputs to the block diagram of the VI. Indicators display the results of

calculations, and can be used for intermediate check-cases for complex computations.

Figure 4.21 shows the relationship of the Control Palette to the VI front panel.

Control Palette Numeric Controls/Indicators Example of a Front PanelControl PaletteControl Palette Numeric Controls/IndicatorsNumeric Controls/Indicators Example of a Front PanelExample of a Front Panel Figure 4.21 Control Palette/Front Panel

39

2. Block Diagram

The block diagram contains the graphical source code for the VI, and consists of

terminals, functions, and wiring. Every item on the Front Panel appears as a terminal

(i.e. ). Terminals take on the data type of the Control or Indicator that they represent.

Terminals serve as access ports that allow the transfer of information between Front

Panel items and the Block Diagram. For clarity of understanding, several terminals may

be bundled together into clusters. User defined inputs are manipulated by functions

within the Block Diagram, and the results of these calculations are returned to Indicators

on the Front Panel. Wires represent the connections between Block Diagram items.

Figure 4.22 shows the Block Diagram corresponding to the previous example VI.

Figure 4.22 Example Block Diagram

3. Icon/Connector Panel

Once the Virtual Instrument is created, the Icon ( ) serves as the graphical

representation of the VI. The Icon can be edited so as to provide an obvious explanation

of its function. This is extremely useful when embedding VIs within other Virtual

Instruments.

The Connector Pane is the interface between the sub-VI and the Controls and

Indicators located on the calling VI’s Front Panel. The Connector Pane shows what type

of inputs and outputs need to be wired to the terminals in order for the VI to function.

Figure 4.23 provides a representation of terminal wiring for the example VI.

40

ConnectorPaneConnectorPaneConnectorPane

Figure 4.23 Example of Connector Pane Wiring

H. DEVELOPMENT OF SIMULATION TOOL

In order to create the launch simulation, it was first necessary to create various

ancillary VIs that would be needed. Some of these instruments were used off-line from

the actual simulation, providing a means of testing new ideas before changing the main

body of code. A modular design philosophy allowed for a significant reuse of previously

designed coding. The virtual instruments created can be categorized as performing one

of three functions: data input/output, data manipulation, and presentation of results.

While it would be tedious and excessive to cover every function-call of every VI,

stepping through the calls made by the Launch_Sim_Autopilot.vi will provide a greater

understanding of the components that comprise this main analysis tool. The overall

process flow is depicted in Figure 4.24.

Read AeroData

EstablishInitial

Conditions

EstablishAutopilot

Commands

PropagateState Vector

ComputeLaunch

Diagnostics

GenerateGraphs

UserInputs

Stage?

StartLaunch_Sim_Autopilot

End

CalculateOrbital

Elements

NOYES

CalculateLift/Drag

Read AeroData

EstablishInitial

Conditions

EstablishAutopilot

Commands

PropagateState Vector

ComputeLaunch

Diagnostics

GenerateGraphs

UserInputs

Stage?

StartLaunch_Sim_Autopilot

End

CalculateOrbital

Elements

NOYES

CalculateLift/Drag

Figure 4.24 Process Flow Diagram

41

1. Front Panel Clusters

Launch_Sim_Autopilot.vi brings together data collected and the results of analyses

performed offline by other VIs. The goal was to provide an analysis tool that the user can

use to determine the performance and trajectory options for any launch-stack

configuration. For ease of use, the Front Panel is divided into four functional areas or

clusters: Setup, Autopilot/Waypoint Control, Dynamic Controls/Indications, and Orbital

Plots.

a. Setup Cluster

The Setup cluster, depicted in Figure 4.25, brings together the

aerodynamic model, vehicle propulsion data, and launch site and initial trajectory

information. Based on this information, the resultant initial conditions are determined.

The user is able to select the method of integration used. A launch diagnostics module is

included in order to help determine the changes in velocity (delta V) that are needed in

order to improve the vehicle’s ability to attain orbit compared to past simulation runs.

b. Autopilot/Waypoint Cluster

The Autopilot/Waypoint Control cluster (Figure 4.26) allows the user to define

initial values, weights, and auxiliary outputs for the automatic pitch and throttle controls.

Additional inputs are the initial and final pitch values, the target point for stage one

burnout, the intermediate waypoints (based upon Mach) and the associated commanded

pitch change. An XY-graph is included to visually depict pitch angle vs. time data. All

of the inputs feed into the Launch_Sim-Autopilot.vi to enable the user to define

trajectories in a much easier and intuitive fashion than is possible using current trajectory

design programs such as POST.

42

Figure 4.25 Setup Cluster

Figure 4.26 Autopilot/Waypoint Control Cluster

c. Dynamic Controls/Indications Cluster

The Dynamic Controls/Indications cluster (Figure 4.27) contains the pitch,

roll, throttle, autopilot, and master run/stop controls. Indicators include the current state

vector, external forces, instantaneous orbital and atmospheric trajectory elements,

commanded pitch and throttle settings, and elapsed simulation time (in sec). Plots depict

altitude vs. downrange, and altitude vs. Mach data of the resultant vehicle trajectory.

Lines of constant barq are included in order to provide a visual reference to the ideal

trajectory.

Figure 4.28 depicts the two different methods of displaying the orbital

path within the Orbital Paths cluster. While its use is unimportant during the launch

phase of operations, the vehicle position within the orbital plane is vital when executing

post-launch orbital insertion maneuvers. The geocentric ground-trace aids launch

planners in determining quickly whether a planned launch azimuth will come close to

population centers. Together, these two visual depictions of position within the orbital

plane provide quick, easily interpreted indications of the vehicle’s current position, as

well as its ability to attain orbit.

43

Figure 4.27 Dynamic Controls/Indications Cluster

Figure 4.28 Orbital Plane/Geocentric Ground Trace

2. Order of Execution

When the Run button on the Front Panel of Launch_Sim_Autopilot.vi is activated,

the contents of each frame are activated in succession. The first frame contains the

Initial_Conditions.vi. This retrieves the launch site, initial trajectory, and propulsion

stage data, and calculates the launch initial conditions; launch velocity components, and

initial orbital elements. The VI Diagram is depicted in Figure 4.29. These data are in

turn used to calculate the velocity boost at the launch site due to the rotation of the earth,

as well as computing the initial x/y coordinates for plotting.

The second frame contains Constant_qbar_lines.vi. This VI takes the target point

for SCRAMJET activation as input and plots the lines of constant barq as overlays on the

altitude vs. Mach graph.

44

Figure 4.29 Initial_Conditions.vi Diagram

The third frame reads in the aerodynamic data using the VI called

Read_aero_data.vi. This retrieves the aerodynamic data file that was created off-line

using AeroCFD/HyperCFD. The data are retrieved from the file location and are

manipulated into the output aero data array (Figure 4.30). This array serves as one of the

inputs to the autopilot VI.

Figure 4.30 Read_aero_data.vi

The remaining sub-frames of the Launch_Sim_Autopilot.vi are dependent upon

the previously collected data. Table 4.1 gives a quick snapshot of the functionality of

each frame. Sub-frames 0, 1, 2, and 5 will be covered in more detail.

a. Sub-frame 0

Sub-frame 0 is where the autopilot calculations are performed. Figure

4.31 depicts the dataflow for the major features of the frame. Autopilot.vi receives input

from the input clusters (Initial Conditions, Spacecraft Controls, Atmospheric Trajectory

Elements, External Forces, Simulation Controls, and Autopilot Aux. Initial Values and

Weights). A logical case structure contains a provision for utilizing waypoints during

flight. Vehicle pitch can be commanded to target values occurring at discrete Mach

45

values. The VI then calculates the output clusters (auxiliary state vector, and autopilot

controls), which serve as inputs for successive frames.

Sub-frame Function

0[0..7] Autopilot Calculations

1[0..7] Propagate the State Vector

2[0..7] Launch Diagnostics

3[0..7] Plot S/C Posn. in Orbital Plane

4[0..7] Plot Alt. vs. Downrange

5[0..7] Manage S/C Mass

6[0..7] Plot Geocentric Lat./Long.

7[0..7] Plot Alt. vs. Mach Table 4.1 VI Frame Functions

Inputs

Outputs

Figure 4.31 Sub-frame 0 (Autopilot Calculations)

Figure 4.32 depicts the data-flow for the state vector propagator. The user

selects between Runge-Kutta and Trapezoidal rule for the method of integration to be

used. When Runge-Kutta is selected, the propagator predicts the values of k1, k2, k3, k4

in order to determine the fourth-order state vector:

µ µ [ ]1 1 2 3 42 26

k kt

X X k k k k+∆

= + + + + (4.23)

46

The Trapezoidal Rule first predicts the state vector using explicit Euler Integrations,

µ ( )1k k k kX X t X X+ = + ∆ ⋅i

(4.24)

then corrects the state vector:

( )·

( )1 1 12k k k k k k

tX X X X X X+ + +

∆= + +

i i (4.25)

The selected propagator VI receives input from Initial Conditions,

Autopilot Controls, Propulsion Stage Data, Aero Data, as well as selected values from

Initial Orbital Elements (Ω, i, ω), and Simulation Controls (simulation time-step).

OutputsInputs

OutputsOutputsInputs

Figure 4.32 Sub-frame 1 (Propagate State Vector)

Embedded within each propagator VI, is forces_xdot.vi. This VI performs the orbital and

atmospheric calculations, calculates the altitude variable thrust and mass-flow, computes

the gravitational force, aerodynamic force coefficients and Lift/Drag forces, and Xi

. A

complete derivation of the equations necessary for transforming from the perifocal to the

inertial plane, deriving the orbital elements, and establishing the initial conditions is

provided in Appendix A.

b. Sub-frame 2

Sub-frame 2 (Launch Diagnostics), depicted in Figure 4.33, performs

launch diagnostics. It computes perigee and apogee altitudes and remaining propellant

47

mass. This provides the user with an instantaneous view of key parameters, with which

they will be better able to determine the launch vehicle’s ability to achieve orbit.

Figure 4.33 Sub-frame 2(Launch Diagnostics)

c. Sub-frame 5

Sub-frame 5 (Manage S/C Mass), depicted in Figure 4.34, manages the

launch vehicle’s mass during the staging process. The Launch Diagnostics cluster is tied

to a Boolean case structure. Remaining propellant mass is compared to the null case

(depleted fuel). If the value of remaining fuel is 0≤ , then stage burnout has occurred,

the current stage # is incremented by one, and the user is queried whether or not to ignite

the following stage. If the remaining fuel is 0≥ , the stage is still producing thrust, and

the current stage vector is propagated out. Next, a logical AND operation is performed,

Figure 4.34 Sub-frame 5(Manage S/C Mass)

which compares the logical value of the user’s decision and whether remaining vehicle

stages exist. A result of TRUE updates the propagated state vector. A result of FALSE

displays a message (Figure 4.35) stating the vehicle failed to achieve orbit.

48

Figure 4.35 User Dialog Box

3. Using Launch_sim_autopilot

A real-world example was chosen to illustrate the operation of

Launch_Sim_Autopilot.vi. NASA’s hypersonic X-43A test vehicle was selected for

several reasons. First, the X-43 represents the most developed US hypersonic vehicle

design. Technical specifications for the X-43 and its Orbital Science Corporation

Pegasus booster were readily available in aerospace literature. Also, Dryden Flight

Research Center had expressed an interest in using the simulations trajectory design

feature to determine possible flight profiles for the future flights of the X-43B and X-43C

variants. Both generic and Hyper-X specific aerodynamic models were utilized in

validating the launch simulation. The results were very similar for each model.

The Reagan Test Site, Kwajelein Atoll was chosen as the launch point. The

Pegasus launch system had previously operated from the site, and its location at 9o North

latitude provides an increase in the “delta-V” of the launch vehicle of approximately 0.46

km/s when launched in the direction of earth rotation. An easterly launch trajectory was

chosen for the Reagan Test Site.

a. Pegasus Launch System

Pegasus is a commercial launch system developed by the Orbital Sciences

Corporation. The system consists of the air-launched Pegasus rocket, and its Orbital

Carrier Aircraft (OCA), dubbed the “Stargazer,” which is a Lockheed L-1011

commercial transport aircraft modified to carry the air-launched Pegasus rocket. This

arrangement provides for improved performance over conventionally launched vehicles

49

of the same size. It also enables the Pegasus to operate from any location with a suitable

airfield. Launch costs are on the order of $12-15 Million USD.

A specially modified first stage of the Pegasus XL was used in the launch

stack configuration. The second stage of the configuration consisted of the X-43 test

vehicle. The modified Pegasus first stage booster, with the X-43A craft mounted to its

nose, was carried by NASA's B-52 jet (Figure 4.36).

Figure 4.36 X-43 Launch Configuration

Performance and mass information for the Pegasus 1st stage was taken

from the International Reference Guide to Space Launch Systems [AIAA 3rd Ed.].

Similar information for the X-43 test vehicle was obtained from Dr. Stephen Whitmore,

at NASA Dryden Flight Research Center [Whitmore]. The propulsion stage information

for all stack components is depicted in Figure 4.37.

Figure 4.37 Propulsion Stage Data

50

b. Launch Trajectory

An easterly launch trajectory was chosen for the Reagan Test Site (Figure

4.38). The Reagan Test Site encompasses approximately 750,000 square miles, although

the total land area is only about 70 square miles. Its location at 9o North Latitude

provides an increase in the “delta-V” of the launch vehicle of approximately 0.46 km/s

when launched in the direction of earth rotation. Also, Orbital Sciences Corporation

Figure 4.38 Reagan Test Site

had previously conducted the launch of the High Energy Transient Experiment (HETE) II

spacecraft from RTS on October 9, 2000 [Ray].

Geographic coordinates of 9.00o N, and 166.08o E were chosen for the

launch point. Launch altitude was taken to be 6.32 km. Launch airspeed of 0.16 km/s, a

launch azimuth of due east, and a flight-path angle of 2o were chosen as initial trajectory

elements. Figure 4.39 depicts the Autopilot/Waypoint Control Cluster settings used for

the RTS launch.

Figure 4.39 Autopilot/Waypoint Control Cluster

51

All inputs were fed into Launch_Sim_Autopilot.VI. The simulation was

programmed to intercept the 1000 psf barq line after launch. With the autopilot engaged,

stage one burnout occurred at an altitude of 32.6 km, at a velocity of Mach 9.43. The

maximum cross loading of the vehicle was 106 psf. The plot of the trajectory from

launch to stage one burnout is given in Figure 4.40.

Figure 4.40 RTS Launch Trajectory (Default Aero)

Utilizing the X-43 specific aerodynamic data, stage one burnout occurred

at an altitude of 37.9 km, at a velocity of Mach 10.3. The maximum cross loading of the

vehicle was 374 psf. The plot of the trajectory from launch to stage one burnout is given

in Figure 4.41.

Figure 4.41 RTS Launch Trajectory (X-43 Aero)

52


53

V. ANALYSIS CASE STUDY

A. METHODOLOGY

In an effort to qualitatively show the potential performance benefits of including a

scramjet within the launch vehicle stack, several case studies were conducted. A

standard configuration Atlas III was chosen for the baseline expendable launch vehicle.

A modified Atlas III, incorporating an axis-symmetric scramjet engine, was to illustrate

the performance of a scramjet enabled design.

To address the possible economic benefits of incorporating scramjet technology,

three cases were used. As in the performance section, the baseline Atlas III and scramjet

enabled Atlas III launch vehicles, were considered. A third economic case was selected

as well, wherein the Atlas III was assumed to be partially reusable.

B. INITIAL CONDITIONS

For the purpose of this analysis, all vehicles were assumed to launch from the

geographic coordinates of 27.5o N Latitude, and 80.0o W Longitude. Launch azimuth

was chosen as due east, in order to take advantage of the increase in “delta-V” due to

launching in the direction of the earth’s rotation. Each vehicle design incorporates a

“mission payload” (payload + structure + fuel) of 4000kg, which is to be delivered into

orbit. Figure 5.1 depicts the propulsion stage characteristics of the Atlas III first stage

that served as the backbone for each of the launch vehicle designs.

Figure 5.1 Atlas III 1st Stage Characteristics

One of several important points to consider is that while both vehicles utilize the

same first stage, there are constraints placed upon the scramjet-enabled design that the

54

Atlas III is not subject to. The Atlas III quickly climbs out of the atmosphere, whereas

the Atlas III-SCRAM must follow along the 1000 psf pressure ( )barq profile in order to

ensure ignition of the scramjet. Also, the Atlas III is able to modulate throttle/pitch

settings in order to arrive at the desired apogee altitude. The Atlas III-SCRAM must fly

the prescribed profile until the fuel is expended. Once the apogee altitude is attained, a

final boost is required to circularize the orbit.

C. ATLAS III

1. Configuration Data

The Atlas III vehicle (Figure 5.2) is an improved version of the established Atlas

II family of launch vehicles. The 1st stage incorporates a single NPO Energomash RD-

180 engine. Two versions of the Atlas III are currently available, with differences only in

the number of engines in the Centaur stage.

Atlas IIIHeight: 28.91m

Diameter: 3.05m

Total Launch Mass: 177,807kg

Dry Mass: 19,907kg

Pmf: 7.93

Figure 5.2 Atlas III

The Atlas IIIA has a single RL-10A-4-2 engine powering the Centaur upper stage while

the Atlas IIIB has two RL-10A-4-2 engines and a stretched Centaur upper stage to

increase geosynchronous transfer orbit delivery performance to just under 10,000 lb.

International Launch Services (ILS) is marketing both vehicles [Atlas III]. Figure 5.3

depicts the propulsion data for the upper stage.

55

Figure 5.3 Centaur Upper Stage

2. Trajectory Design

Initially, two different orbits were selected for designing the conventional Atlas

III trajectories. The first was to a final low earth orbit (LEO) of 165km, and the second

envisioned a re-supply mission to the International Space Station (ISS). Both utilized the

autopilot designed into the launch simulation.

After initial analysis, it was found that the conventional Atlas III was unable to

cost effectively achieve the LEO target. At stage 1 burnout, the Atlas III has already

achieved an apogee altitude of 200km. Re-supplying the ISS was chosen as the baseline

mission for analysis purposes. The space station maintains an orbit between 362-476km

[ISS]. A target orbit of 425km was selected.

Figure 5.4 depicts the ISS service mission trajectory for the Atlas III. The target

point for stage one burnout and waypoints used are depicted in Figure 5.5. For each

chosen Mach break point, there is a corresponding commanded pitch angle ( )cθ . The

autopilot initial values and weighting factors used in the trajectory design are shown in

figure 5.6.

56

Figure 5.4 Atlas III ISS Service Trajectory

Figure 5.5 Autopilot Waypoint Values

Figure 5.6 Autopilot Weights/Initial Values

3. Highlights

The following section performs the mathematical portion of the analysis of the

Atlas III performance. The amount of “delta-V” achieved is given at stage one and two

burnout. Also, the final velocity change to circularize the final orbit is determined.

a. Stage 1 Burnout

Figure 5.7 depicts the altitude/velocity profile of the Atlas III at the time

of stage one burnout. Stage one burnout occurs at an altitude of 81.0466km. At the time

57

of engine burnout, the Atlas III is traveling at Mach 17.879 (4.999km/s). The vehicle has

traveled a downrange distance of more than 120km.

Figure 5.7 Atlas III Stage One Burnout

b. Stage 2 Burnout

Figure 5.8 depicts the altitude/velocity profile of the Atlas III at the time

of stage two burnout. Stage two burns out at an altitude of 95.538km. At the time of

engine burnout, the Atlas III is traveling at Mach 24.3619 (6.750km/s). The vehicle has

traveled a total downrange distance just shy of 200km.

Figure 5.8 Atlas III Stage Two Burnout

c. Apogee Burn

Once the second stage burns out, the remaining mission payload enters a coast

phase. Airspeed is traded for altitude until the payload reaches apogee (Figure 5.9). The

final step is to determine the amount of “delta-V” that an apogee kick motor (AKM)

would have to provide in order to circularize the orbit and keep the payload from

reentering the earth’s atmosphere.

58

Figure 5.9 Atlas III Apogee Altitude

The velocity of the vehicle can be broken down into radial and tangential components,

rVV V

VR ν

µ = ⇒ =

v (5.1)

The change in velocity can then be expressed as:

r

orbit

V

VV

Rνµ

∆ = −

v (5.2)

where: 3

52earth's gravitational parameter 3.986 10

kmx

sµ = =

R orbital radius 6371.00orbit km h= = +

Deriving an expression for the “delta-V” required for circularizing the final orbit results

in:

2

2r

orbit

V V VRν

µ ∆ = + −

(5.3)

59

At apogee, 0rV ≅ , and 6.735036km

Vsν = . Substituting numerical values into the above

equation yields the following expression for the required “delta-V”:

( )

23

523.986 10

0 6.735036 0.92306371 425.85

kmxkm kmsV

s km s

∆ = + − =

+

Now that we know the amount of “delta-V” necessary to circularize our final

orbit, it remains to be determined what amount of fuel is require for this task. This takes

us back to the now familiar rocket equation. In its simple form, the rocket equation is:

0 ln initialsp

final

mV I g

m

∆ = ⋅ ⋅

(5.4)

where: dry pay fuelinitial

final dry pay

m m mmm m m

+ += +

spI is the specific impulse of the rocket engine (sec)

0 2gravitational acceleration at sea level 9.81m

gs

= =

This expression can be further refined into an expression for the propellant mass-fraction

( mfP ):

1dry pay fuel dry pay fuelmf

dry pay dry pay dry pay

m m m m m mP

m m m m m m+ + +

= + = ++ + +

(5.5)

With some simple algebraic manipulation, we come up with the following expression for

the rocket equation in terms of the mfP :

0 1sp

VI g

mfP e

∆ ⋅

= −

(5.6)

60

The spI of the AKM’s engine is assumed to be 300 sec. Substituting this into the above

equation yields a numeric fraction for the amount of fuel required:

( ) 2

0.9230

300 .00981

1 0.368

kms

kms

smfP e

⋅

= − =

With a mission payload mass of 4000kg, the amount of fuel required to produce the

necessary “delta-V” to circularize the orbit is:

40004000 1076.14

0.368 3.717fuel

fuel fuel

m kgm kg m kg+ = ⇒ = =

D. ATLAS III-SCRAM

1. Configuration Data

The Atlas III-Scramjet (Figure 5.10) design shares the same 1st stage as the

conventional Atlas III launch vehicle. That is where the design changes radically from

the Atlas III. The second stage of the Atlas III-SCRAM incorporates a notional axis-

symmetric scramjet design. The engine is mounted ahead of the payload module. Once

first stage burnout occurs, the scramjet will in-effect function as a tugboat, pulling the

payload into space.

Height: 28.91m

Diameter: 3.05m

Total Launch Mass: 93,752kg

Dry Mass: 20,807kg

Pmf: 3.51

Atlas III-SCRAM

Figure 5.10 Atlas III-SCRAM

61

2. Trajectory Design

Again, re-supply of the ISS was chosen as the baseline mission for analysis

purposes. A target orbit of 425km was selected. In addition, a Low Earth Orbit (LEO)

mission was chosen in an effort to showcase the operational flexibility of a scramjet-

enabled launch vehicle. For this mission, an orbital altitude of 165km was chosen.

In order for a scramjet to operate in the most efficient manner, it is necessary for

the vehicle to fly a constant pressure profile. The piloted simulation enabled rapid

investigation of candidate profiles to be investigated in the time it would take

conventional trajectory programs to test a single design. Once an intuitive feel was

obtained, smarter starting values for autopilot weights, and waypoint selection could be

rapidly achieved.

Figure 5.11 describes the trajectory for the Atlas III-SCRAM in terms of Mach #,

and altitude. It is important to understand what information the figure is describing. As

the vehicle passes through the Stratosphere (~45km), the temperature of the air drops

rapidly. This leads to a decreased sonic velocity and (recalling Equation 2.2) therefore an

increase in Mach #. The target point for stage one burnout and waypoints used are

depicted in Figure 5.12. The autopilot initial values and weighting factors used in the

trajectory design are shown in figure 5.13. These are valid for both of the trajectories as

the scramjet flies a constant pressure profile.

Figure 5.11 Atlas III-SCRAM Trajectory

62

Figure 5.12 Autopilot Waypoint Values

Figure 5.13 Autopilot Weights/Initial Values

3. ISS Mission Highlights

The ISS servicing mission necessitated specific fuel loading for both the first and

second stages of the Atlas III-SCRAM. Fuel had to be offloaded from the first stage in

order to achieve the pressure profile for the scramjet, without over stressing the vehicle.

Figure 5.14 depicts the propulsion characteristics for the first stage. Figure 5.15 depicts

the same information for the second stage (scramjet).

Figure 5.14 Stage One Propulsion Data

63

Figure 5.15 Stage Two Propulsion Data

a. Stage 1 Burnout

Figure 5.16 depicts the altitude/velocity profile of the Atlas III-SCRAM at

the time of stage one burnout. Stage one burnout occurs at an altitude of 33.6463km. At

the time of engine burnout, the Atlas III-SCRAM is traveling at Mach 10.3259

(3.16151km/s). The vehicle has traveled a downrange distance of 87km.

Figure 5.16 ISS Mission Stage One Burnout

b. Stage 2 Burnout


the time of stage two burnout. Stage two burns out at an altitude of 45.9466km. At the

time of engine burnout, the Atlas III-SCRAM is traveling at Mach 23.4387

(7.69348km/s). The vehicle has traveled a total downrange distance of 417km.

Appendix B provides a comparative table of performance data for both the Atlas III and

Atlas III-SCRAM vehicles. Although the scramjet burned out at a lower altitude and

Mach number, it’s velocity was greater by almost 1 km/s, and it’s total specific energy is

higher than the conventional Atlas III at this same point.

64

Figure 5.17 ISS Mission Stage Two Burnout

c. Apogee Burn


phase. Airspeed is traded for altitude until the payload reaches the apogee altitude of 425

km (Figure 5.18). For the target altitude, 0rV ≅ , and 7.539123km

Vsν = .

Figure 5.18 ISS Mission Apogee Altitude

We find that the “delta-V” necessary to circularize the final orbit at ISS mean orbital

altitude is:

( )

23

523.986 10

0 7.539123 0.119346371 425.01

kmxkm kmsV

s km s

∆ = + − =

+

65

This results in a mfP of:

( ) 2

.11934

300 .00981

1 0.04138

kms

kms

smfP e

⋅

= − =

Finally, it is determined that the amount of fuel needed to stabilize at a final orbital

altitude of 425km is:

4000

4000 158.9430.04138 25.166

fuelfuel fuel


4. LEO Mission Highlights

For the LEO example, fuel loading of the scramjet stage was selected in order to

deliver the vehicle’s payload into an orbit with a 165km apogee altitude. Figure 5.19

depicts the propulsion characteristics for the first stage. Figure 5.20 depicts the same

information for the second stage (scramjet). Once again, the amount of “delta-V”

achieved at stage one and stage two burnout is given. Also, the final velocity change to

circularize the final orbit is determined.

Figure 5.19 Stage One Propulsion Data

66

Figure 5.20 Stage Two Propulsion Data

a. Stage 1 Burnout


the time of stage one burnout. Stage one burnout occurs at an altitude of 33.7639km. At

the time of engine burnout, the Atlas III-SCRAM is traveling at Mach 10.3806

(3.181km/s). The vehicle has traveled a downrange distance of 87km.

Figure 5.21 LEO Mission Stage One Burnout

b. Stage 2 Burnout


the time of stage two burnout. Stage two burns out at an altitude of 45.9466km. At the

time of engine burnout, the Atlas III-SCRAM is traveling at Mach 23.2849

(7.63842km/s). The vehicle has traveled a total downrange distance of 420km.

67

Figure 5.22 LEO Mission Stage Two Burnout

c. Apogee Burn


phase. Airspeed is traded for altitude until the payload reaches the apogee altitude of

165km (Figure 5.23).

Figure 5.23 LEO Mission Apogee Altitude

At apogee, 0rV ≅ , and 7.738096km

Vsν = . Substituting numerical values into the

previously presented equation yields the following expression for the required “delta-V”:

( )

23

523.986 10

0 7.738096 0.07126371 165

kmxkm kmsV

s km s

∆ = + − =

+

68

Now that we know the amount of “delta-V” necessary to circularize our final

orbit, the amount of fuel required for this task must be determined. The spI of the

vehicle’s engine is assumed to be 300 sec. Substituting this into the equation for mfP

yields a numeric fraction for the amount of fuel required:

( ) 2

.0712

300 .00981

1 0.0245

kms

kms

smfP e

⋅

= − =

With a mission payload mass of 4000kg, the amount of fuel required to produce the

necessary “delta-V” to circularize the orbit is:

40004000 95.7

0.0245 41.816fuel

fuel fuel


E. CONCLUSIONS

1. Performance Basis

The scramjet-enabled design is inherently more flexible than the conventional

Atlas III design. With a small increase in fuel for the scramjet stage, apogee altitude can

be raised by a factor of more that 2.5. This enables the Atlas III-SCRAM design to

deliver payloads to orbital altitudes throughout LEO and into the beginning of the MEO

region. The Atlas III is designed to inject payloads into geo-transfer orbits (GTO). The

station-servicing scenario assumes that the Centaur upper stage of the Atlas III can be

defueled by the described amount, without an adverse affect upon the vehicle’s stability.

Table 5.1 summarizes the orbital insertion requirements for the two designs with respect

to the different orbital profiles.

Atlas III/ Atlas III/ Atlas IIISCRAM SCRAM

Apogee Alt. (km) 165 425 425Prop. Mass Fraction 0.0245 0.04138 0.368

Prop. Mass (kg) 95.7 158.943 1076.02 Table 5.1 Final Orbit Insertion Requirements

69

In the envisioned launch configurations for each vehicle, the Atlas III-SCRAM

would have a total launch mass of 93,752kg, compared to a launch mass of 177,807kg for

the Atlas III. The Atlas III-SCRAM would have a higher dry mass (20,807kg) than the

Atlas III (19,907kg). This is due to the weight of the scramjet module and associated

support systems. mfP for the Atlas III-SCRAM is calculated as mfP = 3.51. The Atlas III,

sitting on the launch pad, has a mfP = 7.93. Table 5.2 summarizes the above results. The

greater dry mass for the Atlas III-SCRAM accounts for the weight of thermal protection.

Atlas III-SCRAM Atlas IIITotal Launch Mass (kg) 93,752 177,807

Dry Mass (kg) 20,807 19,907Prop. Mass Fraction 3.51 7.93

Table 5.2 Comparison of Launcher Characteristics 2. Economic Basis

There is a rule of thumb that says that launch vehicle cost is proportional to the

propellant mass fraction. This provides a back-of-the-envelope check when determining

launch vehicle cost. This is only useful as a rough-cut for budgetary exercises.

Based upon open source information, the Federal Aviation Administration (FAA)

estimates a price range for commercial Atlas III launch services of $90-105 million

[AIAA 3rd Edition]. Lockheed Martin has previously absorbed the development costs of

the Atlas III. The development costs of the scramjet-enabled design could be in the range

of $700-900 million [Davis]. Until commercial customers consider the design “mature”,

it is likely that the cost per launch of the Atlas III-SCRAM design would exceed that of

the Atlas III.

It is difficult to determine what, if any thing would be gained by incorporating

reusability into the Atlas III-SCRAM design. The assumption is made that since

Lockheed-Martin did not incorporate reusable features into its Atlas III, the judgment

must have been made that this offered very little return on investment. This does not

preclude incorporating reusability into the Atlas III-SCRAM design, but it does provide a

starting point for design features.

70

3. Censere Universus

It has been shown that fuel and oxidizer are the two greatest components of the

weight of a launch vehicle. Inclusion of a scramjet removes the need to carry oxidizer for

combustion of the fuel. By virtue of this, spI is increased by a factor of 7, dependent

upon the fuel mixture used. Equivalently, using atmospheric oxygen as the oxidizer

allows the engine to produce the same amount of thrust while using 1/7 the amount of

propellant.

The scramjet-enabled design was able to deliver the mission payload to a variety

of orbits, with a total launch vehicle mass much less than the standard Atlas III. What

falls out of this analysis is that scramjets provide the potential to put lager customer

payloads into orbit than are possible with a conventional design, or that a scramjet-

enabled vehicle that has a much smaller first stage can loft the same payload as larger

conventional configurations.

Because it is unlikely that NASA would be able to dedicate the funds necessary to

establish a new scramjet development program, it will be necessary for industry to do so.

Until the commercial launch sector determines that it is in their best interest to deviate

from the conventional means of building rockets, the performance benefits of scramjet

technology will not be realized, or leveraged in an effort to reduce the cost of space

launch.

71

VI. FUTURE WORK

A. INTRO

This thesis addressed the feasibility of incorporating scramjet technology into an

expendable launch vehicle. In order for this vision to become reality, further research is

needed in the areas of Computational Fluid Dynamics (CFD), vehicle stability, as well as

thermal/acoustic stresses and dynamic loading.

The primary concerns are vehicle controllability, the stresses such a vehicle would

experience throughout the flight envelope, and the thermal loading it would experience

during long duration high-speed flight through the atmosphere.

Equally as important as the areas of further research that address whether “we can

do it,’ is research that addresses how such technology would be applied. It is left to

future students to determine operational concepts in which the scramjet might offer

B. SCRAMJET DEVELOPMENT PROGRAM

In order to realize the performance potential of incorporating a scramjet into a

launch vehicle stack, a comprehensive program must be developed. This effort would

likely be a multi-national one, taking advantage of the various geographic, political, and

technological strengths of each partner.

The X-15 high-speed flight test program has contributed to the success of US

space activities from the Apollo Lunar program to the Shuttle Orbiter. One reason it was

such a success, was the rate at which flights were conducted. Almost 200 flights were

conducted between the time that the program started in 1959, and the time of the final on

October 24, 1968. In order to gather a similar volume of data regarding flight in the

hypersonic region, a flight schedule on the order of 20 flights a year would be necessary.

This would also require a shift from the “zero-defect” mentality that exists today

in the aerospace industry. The airplane did not make the jump from the Wright Brothers

Flyer to the F-22 Raptor overnight. Small incremental improvements were made over

time, and numerous failures occurred along the way. A test-fly-fix-fly (TF3) approach

would still apply strict attention to detail, but would allow for the pursuit of several

different development paths at the same time.

72

Another idea that could be incorporated would be to adapt surplus munitions that

are being retired by the military. The F-14 Tomcat is scheduled to leave the fleet within

the next 10 years [F-14]. The aircraft serves the Navy in an air superiority, fleet defense,

and precision strike role. One of the many different weapons the Tomcat can employ is

the AIM-54 missile, code-named “Phoenix.” The Phoenix missile is the Navy's only

long-range air-to-air missile. Table 6.1 gives the general characteristics of the Phoenix

missile. By modifying the guidance systems of the Phoenix, it should be possible to

enable the missile to arrive at a particular point in the sky. This would enable it to fulfill

the role of a high-speed flight test vehicle.

Primary Function: Long-range air-launched air intercept missileContractor: Hughes Aircraft Co. and Raytheon Co.Unit Cost: $477,131Power Plant: Solid propellant rocket motor built by HerculesLength: 13 feet (3.9 meters)Weight: 1,024 pounds (460.8 kg)Diameter: 15 inches (38.1 cm)Wing Span: 3 feet (.9 meters)Range: In excess of 100 nautical miles (115 statute miles, 184 km)Speed: In excess of 3,000 mph (4,800 kmph)Guidance System: Semi-active and active radar homingWarheads: Proximity fuse, high explosiveWarhead Weight: 135 pounds (60.75 kg)Date Deployed: 1974

Table 6.1 AIM-54 (Phoenix) Characteristics

An axis-symmetric scramjet design would be the best suited for this type of test

vehicle. The designers do not have to contend with the asymmetric loads associated with

body-integrated designs. The design also helps mitigate the heat build up that will result

from travel through the atmosphere.

73

VII. SUMMARY

The goal of this thesis research was to determine the feasibility of scramjet

technology for an intermediate propulsive stage of an expendable launch vehicle. The

reader was first provided with a review of basic concepts necessary for a better

understanding of the assertions made within the thesis. Next a quick overview of US and

international scramjet research efforts was undertaken to provide a broader context.

Detailed information regarding the software programs selected for the development of the

analysis tools, and how these tools were utilized will enable interested parties to

reproduce and validate the conclusions of this thesis.

Scramjet technology provides a potential means of significantly reducing the cost

of delivering payloads to orbit. Using atmospheric oxygen as the oxidizer allows the

engine to produce the same amount of thrust while carrying 1/7 the amount of propellant

as conventional rocket engines. However these benefits do not come cheaply. Scramjets

deliver far higher spI values, but they must follow an air-breathing trajectory.

Aerodynamic heating and drag become significant issues. The extra mass required for

heat protection takes away from the payload fraction. Nonetheless, this analysis shows

significant potential gains for the scramjet configuration.

A scramjet-enabled vehicle enjoys greater operational flexibility than

conventional designs. The final orbit of a payload delivered by such a vehicle is

theoretically only limited by the performance of the scramjet stage. By varying the

duration of flight within the atmosphere, useful payload weights can be delivered to

practically any orbital regime. By focusing efforts upon expendable vehicle designs,

these benefits can be realized in the short-term.

Pursuit of an axis-symmetric design could leverage current international research

efforts in supersonic combustion, and avoid the stability and control issues that plague

body-integrated designs. The concepts proposed in this thesis are approaching a

technology readiness level (TRL) at which potential applications of an axis-symmetric

design could be found in the very near term.

74


75

APPENDIX A. DERIVATION OF ALGORITHMIC EQUATIONS

Back in Chapter IV (Launch Simulation), the equations of motion used in the

launch simulation were derived. What remains is to develop the six classical orbital

elements (COEs). Once this is done, rotational matrices will be derived to shift from the

orbital to the inertial plane. Finally, the conditions used to initialize the simulation are

calculated.

The order of presentation may at first seem counter intuitive, but the choice is

completely arbitrary. In the LabView code, in order to project the ground track of the

vehicle, it is necessary to go from the perifocal to the inertial frame for each data frame.

To initialize the simulation, the order of steps is reversed.

A. DERIVATION OF CLASSIC ORBITAL ELEMENTS

Once an expression is obtained for the position and velocity vectors in the orbital

plane, the next step is to derive the six classic orbital elements (COEs): , , , , ,a e i ω νΩ that

define the vehicle’s orbit. All that is needed is the vehicle’s inertial position and velocity,

Rv

and Vv

. Understanding Space, by Jerry Sellers provides an in-depth explanation for

derivation of the COEs.

1. Semi-major Axis, a

In order to determine the semi-major axis of the orbit, the magnitude of the

position and velocity vectors are used. The Vis-Viva equation gives an expression for the

semi-major axis

22

aV

R

µµ

=⋅

− (A.1)

where: ( ) 2 2 2 magnitude of the position vector x y zR km R R R= = + + (A.2)

2 2 2 magnitude of the velocity vectorsec x y z

kmV V V V = = + +

(A.3)

3

52 earth's gravitational parameter 3.986 10

seckm

xµ

= =

76

In order for the orbit to be viable, the value of the semi-major axis should be larger than

the radius of the planet it is orbiting.

2. Eccentricity, e

The eccentricity vector ev relates to the position and velocity vectors by the

expression

21e V R R V V

Rµ

µ = − ⋅ − ⋅ ⋅

v v v vv (A.4)

where: 3

52 earth's gravitational parameter 3.986 10

seckm

xµ

= =

3. Inclination, i

Figure A.1 Inclination

Inclination defines the orientation of the orbit with respect to the Earth’s

equatorial plane. It is the angle between the unit vector, K , through the North Pole, and

the angular momentum vector, hv

.

1ˆ

cosK h

iK h

− ⋅= ⋅

v (A.5)

The angular momentum vector, hv

, is obtained by taking the cross product of the position

and velocity vectors.

h R V= ×v v v

(A.6)

77

4. Right Ascension of the Ascending Node, Ω

Figure A.2 Right Ascension of the Ascending Node

The right ascension of the ascending node (RAAN) defines the point at which the

orbital plane crosses the equatorial plane. It is the angle measured from the vector

defining the 1st point of Aries, I , and the ascending node of the orbit. The ascending

node vector, nv , lies in the equatorial plane, is perpendicular to the polar axis, K , and is

perpendicular to the angular momentum vector, hv

.

ˆn K h= ×vv (A.7)

The dot product is used to determine Ω (the angle between I and nv )

1ˆ

cosI nI n

− ⋅Ω =

⋅

v (A.8)

Because RAAN can range between 0 and 360o o , it is necessary to perform a

quadrant check. Figure A.2 shows the relationship of the ascending node vector and

geocentric equatorial coordinate system. The quadrant can be determined by inspection

of the position of the ascending node vector relative to the J unit vector. If ( )ˆ 0J n⋅ ≥v ,

then 0 180≤ Ω ≤ o . Otherwise, 180 360≤ Ω ≤ o .

78

5. Argument of Perigee, ω

Figure A.3 Argument of Perigee

The argument of perigee defines the periapsis (low point) of the orbit relative to a

fixed line in inertial space. It is measured as the angle between the ascending node vector

and the eccentricity vector. Using the dot product yields the expression for ω

1cosn en e

ω − ⋅ = ⋅

v v (A.9)

The following logical relationship determines the correct quadrant for ω

If ( )ˆ 0K e⋅ ≥v

0 180ω≤ ≤ o Else

180 360ω≤ ≤ o 6. True Anomaly, ν

True anomaly is defined as the angle between the eccentricity vector, ev , and the

position vector Rv

1cose Re R

ν − ⋅= ⋅

vv (A.10)

It is also possible to derive an expression for the true anomaly in terms of the semi-major

axis.

79

( )

2 21

1 11cos 1

1 cos

a e a er

e e Rν

ν−

− − = ⇒ = −+ ⋅

(A.11)

B. COORDINATE SYSTEM TRANSFORMATION

The inertial reference axis is a line that defines a fixed axis system with respect to

inertial space. Figure A.4 depicts the right-handed XYZ coordinate system. The x-axis

Figure A.4 XYZ Coordinate System

points in the direction of the vernal equinox, which serves as the “anchor” for the

coordinate system. The z-axis passes through the geographic north pole of the Earth.

The y-axis completes the system. All axes are perpendicular to each other.

Given the COE set, the vehicle’s position with respect to the inertial axes can be

computed through the use of rotational matrices. Vallado, in Fundamentals of

Astrodynamics & Applications, provides a rigorous derivation of the transformation from

the orbital frame to the inertial frame.

1. Position Vector (Inertial Frame)

A 3x1 matrix represents the position vector in the inertial frame, where

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )

( ) ( )

cos cos sin cos sincos sin sin cos cos

sin sin

x iy R iz i

ν ω ν ων ω ν ω

ν ω

+ Ω − + Ω = + Ω + + Ω +

(A.12)

80

2. Velocity Vector (Inertial Frame)

The following matrix gives the velocity vector in the inertial frame

21

x

y

z

V

Va e

V

µ = × −

(A.13)

( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

cos sin sin cos cos cos sin

cos cos cos cos sin sin sin

cos cos sin

e i e

i e e

e i

ω ν ω ω ν ω

ω ν ω ω ν ω

ω ν ω

− Ω + + + + + Ω + + Ω − + + Ω

+ + −

C. ESTABLISHING INITIAL CONDITIONS

To start, it is necessary to define the initial conditions at launch. Launch position

will be defined in terms of latitude, inertial longitude, and altitude. Figure A.5

graphically depicts the launch position in the Earth centered frame of reference.

Greenwich Meridian

Launch meridian

North Pole

Equator

Vernal Equinox θg

δ

Re

x

z

y

Figure A.5 Geocentric Launch Position

1. Position Vector

In the inertial coordinate system, the launch position in matrix form is

[ ] [ ] [ ][ ] [ ] [ ]

[ ] [ ]

0 0 0

0 0 0

0 0

R cos cosR cos sin

R sin

x earth

y earth

z earthInertial

R hR hR h

λ δλ δ

λ

+ ⋅ ⋅ = + ⋅ ⋅ + ⋅

(A.14)

81

where: R earth is the radius of the earth (km)

0h is launch altitude (km)

0λ is launch latitude (deg)

0δ is launch inertial longitude (deg)

Within the simulation, the radius of the earth was described as a function of

latitude. By considering the earth as an ellipsoid, the radius at any point can be described

in terms of its semi-major and semi-minor axes. Figure A.6 depicts the relationship of

latitude to position on the surface of the ellipse.

Figure A.6 Ellipsoidal Earth Model

2. Velocity Vector

It is desirable to input the velocity in terms of a natural set of coordinates

referenced to the vehicle’s flight path. The velocity vector in polar coordinates is

0V

V γφ

→

v (A.15)

where 0 Earth relative velocity seckm

V =

flight path angle (deg)γ =

launch azimuth (deg)φ =

82

The flight path angle is referenced to the local horizon. It is the angle between the

velocity vector and the local horizon. The launch azimuth is referenced from due north.

The velocity vector can be further expressed in terms of its components

( ) ( )( ) ( )

( )

0

0

0

cos cosRotational velocity

sin cos of Earth

sin

north

east

down

V VV VV V

φ γφ γ

γ

= + −

(A.16)

The boost in velocity due to the rotation of the Earth acts due east, and is expressed as

[ ] ( )( ) 0 0R cosEarth boost earth earthV h λ= + ⋅ Ω (A.17)

where: Earth angular velocity .00007292115sec secearth

rad rad Ω = =

In order to get to the inertial frame, two successive rotations are accomplished.

The final form of the velocity vector (considering the characteristics of the launch site) is

x

y

z Inertial

V

VV

=

(A.18)

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )

( ) ( )

( ) ( )( ) ( ) [ ] ( )

( )

0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0

cos sin sin cos cos cos cossin sin cos sin cos sin cos R cos

cos 0 sin sinearth earth

VV h

V

δ λ δ δ λ φ γδ λ δ δ λ φ γ λ

λ λ γ

− − − − − ⋅ + + Ω − −

83

APPENDIX B. COMPARISION OF ISS MISSION ATLAS III/ ATLAS III-SCRAM PERFORMANCE CHARACTERISTICS

The following tables provide the reader with reference tool for comparing the

Atlas III and the Atlas III-SCRAM’s performance during the ISS re-supply mission. The

selected data points include the initial mass and fuel mass for stage one and two, as well

as the altitude and velocity at which stage burnout occurred.

A. ATLAS III

Atlas III Initial Mass (kg) Propellant Mass (kg)Stage One 177,807 1.5190E+05Stage Two 9,405 3.2250E+03

Table B.1 Atlas III Mass Properties

Atlas III Burnout Alt. (km) Velocity (Mach) Velocity (km/s)Stage One 81.0466 17.879 4.999Stage Two 95.538 24.3619 6.75

Table B.2 Atlas III Performance Characteristics B. ATLAS III-SCRAM

Atlas III-SCRAM Initial Mass (kg) Propellant Mass (kg)Stage One 93,752 6.7500E+04Stage Two 12,157 5.0767E+03

Table B.3 Atlas III-SCRAM Mass Properties

Atlas III-SCRAM Burnout Alt. (km) Velocity (Mach) Velocity (km/s)Stage One 33.6463 10.3259 3.16151Stage Two 45.9466 23.4387 7.69348

Table B.4 Atlas III-SCRAM Performance Characteristics

84


85

APPENDIX C. AERODYNAMIC DATA

The following tables contain the aerodynamic data obtained from AeroCFD and

HyperCFD for the notional launch vehicle. To facilitate easy understanding, the data

were entered into Microsoft Excel.

A. SUBSONIC

All tables are to be read with alpha varying down the left side and values of

Cd/Cn for Mach values of 0, .2, .5, .7, and .8 across the top.

Alpha Cd(0) Cd(.2) Cd(.5) Cd(.7) Cd(.8) Alpha Cn(0) Cn(.2) Cn(.5) Cn(.7) Cn(.8)

0 1.688 1.709 1.844 2.099 2.383 0 0 0 0 0 0 1 1.688 1.709 1.843 2.098 2.382 1 2.801 2.858 3.234 3.922 4.668 2 1.688 1.709 1.843 2.098 2.382 2 2.865 2.924 3.308 4.012 4.775 3 1.689 1.71 1.844 2.098 2.382 3 2.996 3.058 3.46 4.196 4.994 5 1.698 1.718 1.853 2.106 2.388 5 3.458 3.529 3.993 4.842 5.763 8 1.74 1.76 1.894 2.145 2.425 8 4.631 4.726 5.347 6.485 7.718 10 1.797 1.817 1.951 2.201 2.478 10 5.718 5.836 6.602 8.006 9.529

15 2.091 2.112 2.244 2.491 2.762 15 9.396 9.589 10.849 13.156 15.659

Table C.1 Stage I/II (No delta correction)


0 0.574 0.582 0.636 0.737 0.847 0 0 0 0 0 0 1 0.574 0.582 0.636 0.737 0.847 1 1.758 1.794 2.03 2.462 2.93 2 0.574 0.582 0.636 0.737 0.847 2 1.787 1.824 2.063 2.502 2.978 3 0.575 0.583 0.637 0.738 0.848 3 1.842 1.88 2.127 2.579 3.07 5 0.582 0.59 0.644 0.744 0.853 5 2.03 2.072 2.344 2.843 3.384 8 0.611 0.619 0.672 0.771 0.879 8 2.5 2.551 2.886 3.5 4.166 10 0.649 0.657 0.71 0.808 0.915 10 2.93 2.991 3.384 4.103 4.884

15 0.839 0.847 0.899 0.994 1.098 15 4.376 4.466 5.053 6.128 7.293

Table C.2 Stage II (With Fins)

86


0 0.478 0.487 0.541 0.641 0.752 0 0 0 0 0 0 1 0.478 0.487 0.541 0.641 0.751 1 0.001 0.002 0.002 0.002 0.002 2 0.478 0.487 0.541 0.641 0.751 2 0.003 0.003 0.003 0.004 0.005 3 0.479 0.488 0.542 0.642 0.752 3 0.004 0.005 0.005 0.006 0.007 5 0.486 0.494 0.548 0.648 0.757 5 0.007 0.008 0.009 0.01 0.012 8 0.515 0.523 0.577 0.676 0.784 8 0.012 0.012 0.014 0.016 0.02 10 0.553 0.561 0.614 0.713 0.82 10 0.015 0.015 0.017 0.02 0.024

15 0.743 0.751 0.803 0.899 1.002 15 0.021 0.022 0.025 0.03 0.036

Table C.3 Stage II (No Fins)


0 0.096 0.095 0.095 0.096 0.095 0 0 0 0 0 0 1 0.096 0.095 0.095 0.096 0.096 1 1.757 1.792 2.028 2.46 2.928 2 0.096 0.095 0.095 0.096 0.096 2 1.784 1.821 2.06 2.498 2.973 3 0.096 0.095 0.095 0.096 0.096 3 1.838 1.875 2.122 2.573 3.063 5 0.096 0.096 0.096 0.096 0.096 5 2.023 2.064 2.335 2.833 3.372 8 0.096 0.096 0.095 0.095 0.095 8 2.488 2.539 2.872 3.484 4.146 10 0.096 0.096 0.096 0.095 0.095 10 2.915 2.976 3.367 4.083 4.86

15 0.096 0.096 0.096 0.095 0.096 15 4.355 4.444 5.028 6.098 7.257

Table C.4 Delta Calculation (B.2-B.3)


0 1.784 1.804 1.939 2.195 2.478 0 0 0 0 0 0 1 1.784 1.804 1.938 2.194 2.478 1 4.558 4.65 5.262 6.382 7.596 2 1.784 1.804 1.938 2.194 2.478 2 4.649 4.745 5.368 6.51 7.748 3 1.785 1.805 1.939 2.194 2.478 3 4.834 4.933 5.582 6.769 8.057 5 1.794 1.814 1.949 2.202 2.484 5 5.481 5.593 6.328 7.675 9.135 8 1.836 1.856 1.989 2.24 2.52 8 7.119 7.265 8.219 9.969 11.864 10 1.893 1.913 2.047 2.296 2.573 10 8.633 8.812 9.969 12.089 14.389

15 2.187 2.208 2.34 2.586 2.858 15 13.751 14.033 15.877 19.254 22.916

Table C.5 Launch Configuration (B.1+B.4)

87

B. SUPERSONIC

All tables are to be read with alpha varying down the left side and values of

Cd/Cn for Mach values of 1.2, 1.5, 2, 5, 8, and 10 across the top.

Alpha Cd(1.2) Cd(1.5) Cd(2) Cd(5) Cd(8) Cd(10) Alpha Cn(1.2) Cn(1.5) Cn(2) Cn(5) Cn(8) Cn(10)

0 1.0109 0.8888 0.7705 0.549 0.4947 0.4788 0 0 0 0 0 0 0 1 1.0109 0.8888 0.7705 0.549 0.4947 0.4788 1 0.24779 0.11631 0.09585 0.05786 0.048 0.04464

2 1.0109 0.8888 0.7705 0.549 0.4947 0.4788 2 0.49558 0.23261 0.1917 0.11571 0.096 0.08928

5 1.0109 0.8888 0.7705 0.549 0.4947 0.4788 5 1.23894 0.58153 0.47924 0.28929 0.24 0.22321 8 1.0109 0.8888 0.7705 0.549 0.4947 0.4788 8 1.9823 0.93045 0.76679 0.46286 0.38399 0.35713

Table C.6 Stage I/II (No Delta Correction)


0 0.9329 0.8461 0.699 0.4429 0.381 0.3625 0 0 0 0 0 0 0 1 0.9329 0.8461 0.699 0.4429 0.381 0.3625 1 0.24738 0.1159 0.09544 0.05745 0.04759 0.04424 2 0.9329 0.8461 0.699 0.4429 0.381 0.3625 2 0.49477 0.2318 0.19089 0.1149 0.09519 0.08847 5 0.9329 0.8461 0.699 0.4429 0.381 0.3625 5 1.23692 0.57951 0.47722 0.28726 0.23797 0.22118 8 0.9329 0.8461 0.699 0.4429 0.381 0.3625 8 1.97906 0.92721 0.76355 0.45962 0.38076 0.35389

Table C.7 Stage II (With Fins)


0 0.7544 0.6428 0.5678 0.3965 0.3523 0.3396 0 0 0 0 0 0 0 1 0.7544 0.6428 0.5678 0.3965 0.3523 0.3396 1 0.03031 0.03031 0.03031 0.03031 0.03031 0.03031 2 0.7544 0.6428 0.5678 0.3965 0.3523 0.3396 2 0.06062 0.06062 0.06062 0.06062 0.06062 0.06062 5 0.7544 0.6428 0.5678 0.3965 0.3523 0.3396 5 0.15155 0.15155 0.15155 0.15155 0.15155 0.15155 8 0.7544 0.6428 0.5678 0.3965 0.3523 0.3396 8 0.24248 0.24248 0.24248 0.24248 0.24248 0.24248

Table C.8 Stage II (No Fins)


0 0.1785 0.2033 0.1312 0.0464 0.0287 0.0229 0 0 0 0 0 0 0 1 0.1785 0.2033 0.1312 0.0464 0.0287 0.0229 1 0.21707 0.08559 0.06513 0.02714 0.01728 0.01393 2 0.1785 0.2033 0.1312 0.0464 0.0287 0.0229 2 0.43415 0.17118 0.13027 0.05428 0.03457 0.02785 5 0.1785 0.2033 0.1312 0.0464 0.0287 0.0229 5 1.08537 0.42796 0.32567 0.13571 0.08642 0.06963 8 0.1785 0.2033 0.1312 0.0464 0.0287 0.0229 8 1.73658 0.68473 0.52107 0.21714 0.13828 0.11141

Table C.9 Delta Calculation (B.7-B.8)

88


0 1.1894 1.0921 0.9017 0.5954 0.5234 0.5017 0 0 0 0 0 0 0 1 1.1894 1.0921 0.9017 0.5954 0.5234 0.5017 1 0.46486 0.2019 0.16098 0.085 0.06528 0.05857 2 1.1894 1.0921 0.9017 0.5954 0.5234 0.5017 2 0.92973 0.40379 0.32197 0.16999 0.13057 0.11713 5 1.1894 1.0921 0.9017 0.5954 0.5234 0.5017 5 2.32431 1.00949 0.80491 0.425 0.32642 0.29284 8 1.1894 1.0921 0.9017 0.5954 0.5234 0.5017 8 3.71888 1.61518 1.28786 0.68 0.52227 0.46854

Table C.10 Launch Configuration (B.6+B.9)

89

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91

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92

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93

BIBLIOGRAPHY

Isakowitz, Steven J., J.P. Hopkins Jr., J.B. Hopkins, International Reference Guide to

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94


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NASA Dryden Flight Research Center Edwards, California

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